Statistics MCQs Tests - Basic Statistics and Data Analysis.pptx

Statistics Mcqs:
Statistics are expressed?
A. Descriptive
B. Ability
C. Qualitatively
D. Quantitatively
In the plural sense, statistic means ?
A. Methods
B. Data
C. Science
D. Meteorology
The word statistics is defined as _?
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A. Singular Sense
B. Plural Sense
C. Singular as well as plural sense
D. Non of these
Statistics is the backbone of ?
A. Economics
B. Mathematics
C. Research
D. Computer
Use of Statistics in planning is ?
A. Useless
B. Various Methods
C. Unavoidable
D. Samples
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Statistics tests the law of ?
A. Other sciences
B. physics
C. Business
D. Literary subjects
In natural Sciences, statistics .
A. Has no role
B. Average
C. Plays an Important role
D. Study
In statistics, a sample means ?
A. A portion of the sample
B. A portion of the population
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C. All the items under investigation
D. None of the above
A numerical value calculated from sample is called ?
A. Mathematics
B. Economics
C. Statistic
D. None of these
Census reports used as a source of data is ?
A. Primary source
B. secondary source
C. Organized data
D. none
The data collected by NADRA to issue National Identity cards are ?
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A. Official data
B. un-official data
C. Primary data
D. Secondary data
Village Patwari collecting the data about cotton crops is the example of_ ?
A. variable
B. Constant
C. Primary data
D. Secondary data
Statistics has handicap dealing with ?
A. Constant
B. Variable
C. Quantitative data
D. Qualitative data
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Major area of statistics today is concerned with drawing of conclusions from ?
A. Samples
B. Primary
C. Two
D. Complete study
The Number of road accidents is the example of ?
A. variable
B. Constant
C. Discrete variable
D. Continuous variable
In Statistics, a population consists of:_ ?
A. All People living in a country
B. All People living in the are under study
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C. All subjects or objects whose characteristics are being studied
The sum of squares of deviation is least if measure from ?
A. Mean
B. Mode
C. Median
D. Variance
Variance is always calculated from ?
A. Mean
B. Variance
C. Geometric Mean
D. Median
E. Mode
The sum of values divided by their number is called ?
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A. Median
B. Harmonic Mean
C. Mean
D. Mode
E. None of these
Arithmetic Mean is affected by extreme values?
A. Not
B. Highly
C. Less
D. None of these
To find the average speed of a journey which is the appropriate measure of central tendency?
A. Mean
B. Geometric Mean
C. Harmonic Mean
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D. Weighted Mean
E. Mode
If any of the value in data set is negative then it is impossible to compute: ?
A. Arithmetic Mean
B. Harmonic Mean
C. Geometric Mean
D. Mode
E. Median
The most repeated (popular) value in a data set is called ?
A. Median
B. Mean
C. Mode
D. Geometric Mean
E. Harmonic Mean
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Which of the measures given here are based on every item of the series (uses all
observations)?
A: Range
B: Standard Deviation
C: Quartile Deviation
D: All of them
In a distribution of 10, 20, 30, 40, 50, the x is 30, the sum of deviations from x will
be: ?
A: 60
B: 30
C: Zero
D: 15
Questionnaire survey method is used to collect _?
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A. Secondary data
B. Qualitative variable
C. Primary data
D. None of these
A parameter is a measure which is computed from ?
A. Population data
B. Sample data
C. Test statistics
D. None of these
Primary data and data are same?
A. Grouped
B. Secondary data
C. Ungrouped
D. None of these
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The data which have already been collected by some one are called ?
A. Raw data
B. Array data
C. Secondary data
D. Fictitious data
The number of accidents in a city during 2012 is ?
A. Discrete variable
B. Continuous variable
C. Qualitative variable
D. Constant
The weights of students in a college/school is a _?
A. Discrete Variable
B. Continuous Variable
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C. Qualitative Variable
D. None of these
Which of the following divides a group of data into four subgroups?
A. Percentiles
B. Deciles
C. Median
D. Quartiles
E. Standard Deviation
The middle value of an ordered array of numbers is the ?
A. Mode
B. Mean
C. Median
D. Mid Point
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According to the empirical rule, approximately what percent of the data should lie within
μ±σ?
A. 75%
B. 99.7%
C. 90%
D. 95%
Life of a T.V picture tube is a: ?
D. Constant
In descriptive statistics, we study:
A. The description of decision making process
B. The methods for organizing, displaying, and describing data
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C. How to describe the probability distribution
Which branch of statistics deals with the techniques that are used to organize, summarize,
and present the data?
A. Advance Statistics
B. Descriptive Statistics
C. Inferential Statistics
D. Bayesian Statistics
Marital status of an individual is the example of _?
A. Attribute
B. Discrete variable
C. Continuous variable
D. Constant
Proportion becomes percentage when multiplied by ?
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A. 1/10
B. 1/1000
C. 1/100
D. 100
Identify the attribute?
A. Blood group
B. Blood Pressure
C. Temperature of room
D. Religions of people of a country
Age of a shopkeeper is the example of ?
A. Qualitative
B. Quantitative data
C. Variable data
D. Continuous data
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data are collected for the first time.
A. Research
B. Statistical
C. Secondary
D. Primary
A Constant can assume _ value?
A. One
B. Four
C. More than value
D. Resindent
Statistics Laws are true ?
A. In each case
B. Average
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C. Facts
D. Field
Most of the recent developments in statistics arose to meet the needs of ?
A. Biology
B. Three reasons
C. Hands
D. Physics
statistics deals with collection, presentation and analysis of data?
A. Inferential
B. Descriptive
C. Collection
D. Two
used the word statistics for the first time during one of his lectures at a German
university?
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A. Fisher
B. unavoidable
C. Feet
D. Achenwall
A characteristics that does not change is called ?
A. variable
B. Attribute
C. Constant
D. None of these
The word statistics is at present used in ?
A. Two ways
B. Four ways
C. Six ways
D. Three way
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Statistical Laws are valid in the ?
A. Long run
B. Plural sense
C. indefinite
D. Short run
Statistics laws are true for ?
A. Short run
B. Long run
C. Medium period
D. None of these
Dependence of difference on statistics is for _?
A. Two reasons
B. Short run
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C. Three reasons
D. Natural Sciences
Data being used by an agency which is originally collected by them are data?
A. Quantitative
B. Primary
C. Discrete
D. Secondary
Usually measurements give rise to data?
A. Discrete
B. Specific
C. Continuous
D. Constant
Continuous variable can assume value?
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A. All possible
B. Constant
C. Accuracy
D. Specific
Data regarding opinions of consumers about some product obtained through lady workers are
?
A. Cheapest method
B. Existing Sources
C. Primary
D. Secondary
Data published by Bureau of statistics in its publications are ?
A. Secondary data
B. Discrete data
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C. Continuous data
D. None
f1x12 + f2x22 + —————+ fxx42= ?
A. Σu1=1 ƒ ixi2
B. Σni-1 ƒ ixi2
C. Σpi=1 ƒ ixi2
D. Σmi=1 ƒ ixi2
Eyes color of employees is the example of_ ?
A. Continuous variable
B. Constant variable
C. Discrete variable
D. Attribute
Results obtained by counting are _?
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A. Continuous
B. Discrete
C. Both (a) and (b)
D. None of these
making a entrance slip in service hospital is the method of collection of data
by ?
A. Registration
B. Entry
C. Correspondents
D. none of these
You asked five of your classmates about their height. On the basis of this information, you
states the average height of all student in your university or college is 67 inches. This is an
example of ?
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A. Descriptive statistics
B. Inferential Statistics
C. Parameter
D. Population
Which of the following is not based on all the observations ?
A. Arithmetic Mean
B. Geometric Mean
C. Harmonic Mean
D. Weighted Mean
E. Mode
The mean of a distribution is 14 and the standard deviation is 5. What is the value of the
coefficient of variation ?
A. 60.4%
B. 48.3%
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C. 35.7%
D. 27.8%
Which of the following describe the middle part of a group of numbers ?
A. Measure of Variability
B. Measure of Central Tendency
C. Measure of Association
D. Measure of Shape
The mean of a distribution is 23, the median is 24, and the mode is 25.5. It is most likely that
this distribution is ?
A. Positively Skewed
B. Symmetrical
C. Asymptotic
D. Negatively Skewed
The sum of the deviations about the mean is always ?
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A. Range
B. Zero
C. Total Standard Deviation
D. Positive
E. Negative
Which of the following is not a measure of central tendency ?
A. Percentile
B. Quartile
C. Standard deviation
D. Mode
If the standard deviation of a population is 9, the population variance is _?
A. 9
B. 3
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C. 21
D. 81
If a distribution is abnormally tall and peaked, then is can be said that the distribution
is ?
A. Leptokurtic
B. Pyrokurtic
C. Platykurtic
D. Mesokurtic
Sum of dots when two dice are rolled is ?
A. a discrete variable
B. a continuous variable
C. a constant
D. a qualitative variable
Which of these represent qualitative data ?
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A. Height of a student
B. Liking or disliking of (500) persons of a product
C. Income of a government servant in a city
D. Yield from a wheat plot
The first hand and unorganized form of data is called ?
A. Secondary data
B. Organized data
C. Primary data
D. None of these
The grouped data is also called ?
A. Raw data
B. Primary data
C. Secondary data
D. Qualitative data
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Life of a T.V picture tube is a ?
D. Constant
Population census is conducted through ?
A. Sample survey
B. Accounting
C. Investigation
D. Complete enumeration
A chance variation in an observational process is ?
A. Dispersion/ Variability
B. Measurement error
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C. Random error
D. Instrument error
A constant variable can take values ?
A. Zero
B. Fixed
C. Not fixed
D. Nothing
In inferential statistics, we study ?
A. the methods to make decisions about population based on sample results
B. how to make decisions about mean, median, or mode
C. how a sample is obtained from a population
In descriptive statistics, we study ?
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A. The description of decision making process
B. The methods for organizing, displaying, and describing data
C. How to describe the probability distribution
When data are collected in a statistical study for only a portion or subset of all elements of
interest we are using?
A. A sample
B. A Parameter
C. A Population
D. Both b and c
Data in the Population Census Report is ?
A. Grouped data
B. Ungrouped data
C. Secondary data
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D. Primary data
E. Arrayed data
Statistic is a numerical quantity, which is calculated from?
A. Population
B. Sample
C. Data
D. Observations
Which branch of statistics deals with the techniques that are used to organize, summarize,
and present the data?
A. Advanced Statistics
B. Probability Statistics
C. Inferential Statistics
D. Descriptive Statistics
E. Bayesian Statistics
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In statistics, conducting a survey means ?
A. Collecting information from elements
B. Making mathematical calculations
C. Drawing graphs and pictures
Which one is the not measure of dispersion?
A. The Range
B. 50th Percentile
C. Inter-Quartile Range
D. Variance
Which of these is a relative measure of dispersion ?
A. Standard Deviation
B. Variance
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C. Coefficient of Variation
D. None of these
The mean deviation of the values, 18, 12, 15 is ?
A. 6
B. Zero
C. 3
D. 2
In statistics, a sample means ?
A. A portion of the sample
B. A portion of the population
C. all the items under investigation
D. none of the above
The height of a student is 60 inches. This is an example of ?
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A. Qualitative data
B. Categorical data
C. Continuous data
D. Discrete data
Which of the following is not based on all the observations ?
A. Arithmetic Mean
B. Geometric Mean
C. Harmonic Mean
D. Weighted Mean
E. Mode
Which one of the following measurement does not divide a set of observations into equal
parts ?
A. Quartiles
B. Standard Deviations
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C. Percentiles
D. Deciles
E. Median
You asked five of your classmates about their height. On the basis of this information, you
stated that the average height of all students in your university or college is 67 inches. This is
an example of ?
A. Descriptive statistics
B. Inferential Statistics
C. Parameter
D. Population
The algebraic sum of deviations from mean is ?
A. Maximum
B. Zero
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C. Minimum
D. Undefined
A measure of dispersion is always ?
A. Zero
B. Positive
C. Negative
D. Infinity
The measure of dispersion is changed by a change of ?
A. Origin
B. Scale
C. Algebraic Signs
D. None
Mean Deviation, Variance and Standard Deviation of the values 4, 4, 4, 4, 4, 4
is _?
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A. 4
B. 8
C. 2
D. 12
E. 0
The sum of squared deviations of a set of n values from their mean is ?
A. Zero
B. Maximum
C. Least
D. None
Lowest value of variance can be ?
A. 1
B. -1
C. 3

D. -3
E. 0
Variance remains unchanged by change of_ ?
A. Origin
B. Scale
C. Both
D. None of these
?
If a and b are two constants, then Var(a+bX) is
A. a±bVar(X)
B. Var(a)±Var(X)
C. ±bVar(X)
D. b2Var(X)
E. (a±b)Var(X)
Standard deviation is calculated from the Harmonic Mean (HM) ?
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A. Always
B. Sometimes
C. Never
D. None of these
If X and Y are independent then SD (X − Y) is ?
A. SD(X)−SD(Y)
B. SD(X)+SD(Y)
C. SD(X)+SD(Y)−−−−−−−−−−−−−−√
D. Var(X)+Var(Y)−−−−−−−−−−−−−−−√
18) If Y=−8X − 5 and SD of X is 3, then SD of Y is
If the standard deviation of the values 2, 4, 6, 8 is 2.58, then the standard deviation of the
values 4, 6, 8, 10 is ?
A. 0
B. 2.58
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C. 5
D. 4.66
E. 2.33
If all values are same then the measure of dispersion will be ?
A. 1
B. 0
C. Mean
D. Mode
E. Median
is used to compare the variation or dispersion in two or more sets of data even
though they are measured in different units?
A. Range
B. Standard Deviation

D. Mean Deviation
Second moment about mean is ?
B. Variance
D. None of these
The Coefficient of Skewness is always zero for distribution?
A. Symmetrical
B. Skewed
C. All of above
D. None of these
In uni-model distribution, if mode is less than mean ?
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A. Symmetrical
B. Normal
C. Positively Skewed
For Mesokurtic curve of the distribution, β2 is ?
A. Zero
B. 3
C. 3
E. None of these
is based on all observations of data?
A. Median
B. Mode
C. Mean
D. None of these
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If right tail is longer than left tail then distribution is called ?
A. Negatively Skewed
B. Positively Skewed
C. All of above
D. None of these
Lack of symmetry is called ?
A. Absolute Dispersion
B. Relative Dispersion
C. Skewness
D. Non of these
The first moment about means is always ?
A. Zero
B. 1
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C. Negative
D. None of these
If mean is 25 and standard deviation is 5 then C.V (Coefficient of variation)
is ?
A. 100%
B. 25%
C. 20%
D. None of these
The measure of Dispersion can never be ?
A. Positive
B. Negative
C. 0
D. 1
The standard deviation is always than mean deviation?
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A. Greater
B. Less
C. Equal
D. None
The variance of 5 numbers is 10. If each number is divided by 2, then the variance of new
numbers is ?
A. 20
B. 5
C. 2.5
D. 5.5
E. 0
Suppose for 40 observations, the variance is 50. If all the observations are increased by 20, the
variance of these increased observation will be ?
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A. 50
B. 70
C. 50/20
D. 50-20 = 30
E. 50
Var(2X+3) is ?
A. 5 Var(X)
B. 4 Var(X)
C. 4 Var(X)+3
D. 5 Var(X)+3
The variance of a constant is ?
A. Zero
B. Constant
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C. a
D. None
If Y=−8X − 5 and SD of X is 3, then SD of Y is _?
A. 8
B. 3
C. 5
D. 24
E. None
For a symmetrical distribution approximately 68% of the cases are included between
?
A. X¯¯¯¯−S and X¯¯¯¯+S
B. X¯¯¯¯−2S and X¯¯¯¯+2S
C. X¯¯¯¯−3S and X¯¯¯¯+3S
D. None of these

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is used to criterion of consistency i.e for consistence performance?
A. Range
B. Standard Deviation
D. Mean Deviation
If the third moment about mean is zero then distribution is ?
A. Mesokurtic
B. Positively Skewed
C. Symmetrical
Quartile Coefficient of skewness lies between ?
A. 0 and 1
B. -1 and +1
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C. -1 and 0
D. None of these
The degree of peakedness is called ?
A. Dispersion
B. Skewness
C. Symmetry
D. Kurtosis
If β2=m4m22<3, the distribution is called ?
A. Normal
B. Mesokurtic
C. Leptokurtic
D. Platykurtic
The calculation of mean and variance is based on ?
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A. Small values only
B. Large values only
C. Extreme values only
D. All values
Arithmetic mean of two positive numbers “X” and “Y” is ?
A. ab2
B. 2a2
C. (a+b)/2
D. a−b2
E. 2a+b
For a certain distribution if ∑(x−2)=18,∑(x−24)=0,∑(x−28)=−24) then arithmetic mean
is ?
A. 21
B. 24
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C. 28
D. 0
The mean of 10 numbers is 9, then sum of these numbers will be ?
A. 9
B. 0.9
C. 70
D 90
Sum of deviations will be zero if it is taken from ?
A. Mean
B. Mode
C. Median
D. Standard Deviation
The mean of a constant “b” is ?
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A. Zero
B. b
C. None
The average of first n natural numbers is ?
A. n+12
B. n2
C. All of the above
D. None of these
The sum of squared deviation is least from ?
A. Median
B. Mean
C. Mode
D. Standard Deviation
Given the N values in a series, the geometric mean is ?
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A. The third root of the product of N values
B. The square root of the product of N values
C. The fourth root of the product of N values
D. The Nth root of the product of N values
In a frequency distribution the last cumulative frequency is 300, Median shall lie
in ?
A. 140th item
B. 130th item
C. 160th item
D. 150th item
Find the median of the following datA. 160, 180, 200, 280, 300, 320, 400?
A. 140
B. 300
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C. 180
D. 280
The average monthly production of a factory for the first 8 months is 2,500 units, and for the
next 4 months the production was 1,200 units. The average monthly production of the year
will be _?
A. 2066.55 units
B. 5031.10 units
C. 4021.12 units
D. 3012.11 units
In a frequency distribution the last cumulative frequency is 500. Q3 must lie
in ?
A. 275th item
B. 375th item
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C. 150th item
D. 175th item
is the measure of average which can have more than one value?
A. Mean
B. Median
C. Harmonic Mean
D. Mode
E. Geometric Mean
2nd Quartile = 5th Decile = 50th Percentile = ?
A. Mode
B. Median
C. Mean
D. Geometric Mean
E. Harmonic Mean
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Data must be arranged either in ascending or descending order, if some wants to
compute ?
A. Mode
B. Median
C. Harmonic Mean
D. Geometric Mean
E. Median
If any of the value in data set is zero then it is not possible (i.e. impossiblE. to
compute ?
A. Mode
B. Median
C. Mean
D. Harmonic Mean
E. Geometric Mean
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Which of the following cannot be less than zero (negative)?
A. Median
B. Geometric Mean
C. Arithmetic Mean
D. Harmonic Mean
E. Mode
The Geometric Mean of -2, 4, 03, 6, 0 will be ?
A. -3
B. 0
C. 3
D. Cannot be Computed
E. None of these
If 10% is added to each value of variable, the geometric mean of new variable is added
by ?
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A. 5%
B. 10%
C. No Change
D. 110%
E. 90%
Which of the following Measure of Averages is not based on all the values given in the data
set?
A. Arithmetic Mean
B. Geometric Mean
C. Median
D. Mode
E. Both C. and D.
Geometric means of X1 and X2 is ?
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A. X1+X2
B. X1+X2x
C. X1+X2−−−−−−−√
D. X1×X2−−−−−−−√
E. X1−−−√+X2−−−√
Which of the following Measure of averages is affected by extreme (very small or very largE.
values in data set?
A. Geometric Mean
B. Median
C. Arithmetic Mean
D. Harmonic Mean
E. Mode
The Harmonic Mean of any two numbers is ?
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A. a+b2
B. 2aba+b
C. ab−−√
D. a+b
If a distribution has two modes then this distribution is called ?
A. Uni-Modal
B. Bi-Modal
C. Tri-Modal
D. Multi-Modal
E. None of these
In a week the prices of a bag of rice were 350 ,280, 340, 290, 320, 310, 300. The range
is ?
A. 60
B. 90
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C. 70
D. 100
A contractor employs 20 male, 15 female and 5 children in his factory. Male wages are Rs. 10
per day, female Rs. 8 per day, and children Rs. 3 per day. The weighted x of wages paid per
day will be ?
A. 3.86
B. 8.37
C. 9.21
D. 10.63
If x is 4 and the distribution is 2, 3, 4, 5, 6, the sum of squared deviations from the x will
be ?
A. 8
B. 10
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C. 6
D. 12
Discrete random variable is real valued function defined on a _ sample space?
A. Discrete
B. Variable
C. Scale
D. Non of these
If E(x) is the expected value of X then E[x – E(x)]= ?
A. E(x) – E(x)
B. E(X) – 0
C. 0
D. E(x) + E(x)
A random variable may be ?

A. fixed
B. continuous
C. discrete
D. discrete or continuous
Two digit random numbers are ?
A. 2
B. 10
C. 99
D. 100
are the numbers obtained by some random process?
A. Two- digit number take
B. Random table
C. Pack
D. Non of these
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A function probability that a random variable of x has a value less than is called
?
A. Random function
B. Distribution function
C. Continuous function
D. probability function
A random variable is _ ?
A. Not a function
B. A continuous variable
C. A function
D. None of these
The number of defective bulbs in a lot is example of ?
A. Continuous variable
B. Discrete variable
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C. Function
D. None of these
If a & b are constants, then Var (a + bX) equal to ?
A. Var(bX) + a
B. b2 Var(X)
C. b Var(x)
D. None of these
For discrete random ‘X’, the expectation of X i.e., E(x) is equal to: ?
A. ∑P(x)
B. ∑x.P(x)
C. ∑x2P(x)
D. One
A discrete probability distribution may be represented by ?
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A. A Table
B. A Graph
C. A mathematical Equation
D. All of these
The probability function is always_ ?
A. Negative
B. Non Negative
C. Positive
D. None
Probability distribution of a random variable is also know as Probability ?
A. Probability Function
B. Distribution Function
C. Probability Distribution
D. Probability Density Function
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The distribution function F(X) is represent by ?
A. P(X=x)
B. P(X
C. P(X>x)
D. P(X≤x)
For distribution Function F(X),F(-∞)=0 and F(∞)= ?
A. 0
B. -1
C. 1
D. Non of These
For a random variable X, E(X) is _?
A. Harmonic Mean
B. Geometric Mean (GM)
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C. Arithmetic Mean (AM)
D. Non
Probability of occurrence of an event lies between ?
A. -1 and 0
B. 0 and 1
C. -1 and 1
D. exactly 1
For a probability density function (pdf), the probability of a single point is ?
A. 1
B. 2
C. 0
D. Constant
What is the probability that a ball drawn at random from a jar ?
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A. 0.1
B. 1
C. 0.5
D. 0
E. Cannot be determined from given information
If c is non-random variable, the E(C) is ?
A. Zero
B. C
C. 1
D. 2
Coefficient of variation (C.V) is given below: ?
A. Mean/S.D.
B. S.D./Mean x 100
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C. Mean/S.D. x 100
D. S.D./Mean
For two independent random variables X & Y, Var (x ± y)= ?
A. Var(X) + Var (Y)
B. Var(X) – Var (Y)
C. Var (X)±
D. Zero
Var (kY)= ?
A. k Var (Y)
B. k2 Var(Y)
C. Var(Y)
D. k2
Hourly temperature recorded by weather bureau is the example of ?
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B. Qualitative variable
C. Continuous variable
D. None of these
A continuous random variable which can assume all possible values on scale in a given
?
0
A. Interval
B. Point
C. Time
D. Sample space
Random numbers are also called ?
A. Random experiment
B. random Errors
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C. Random digits
D. None of these
A random variable is that whose value is determined by the outcome of ?
A. Trial
B. event
C. Experiment
D. Random experiment
Random numbers are used for selection of ?
A. Random space
B. Space
C. Random sample
D. Non of these
Experiment in which outcomes vary from trial to trial ?
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A. Experiment
B. Variable
C. Random experiment
D. Non of these
The mathematical exception of x + y is equal to ?
A. E(x + 0)
B. E(x + x)
C. E(x) + E(y)
D. E(y)
The basic random numbers are ?
A. 0 and 1
B. 0,1,2,…………9
C. 1,2,3….10
D. None of these
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The variance of randomvariable of x then var(x) = E[x-E[x]2 = E[_ ]?
A. (X – A)2
B. E(x)
C. (x – u)2
D. (x – 4)2
The time taken by an athlete to run a 400 mile race in SAF games ?
A. Continuous data
B. Random
C. Discrete data
D. Non of these
If E (ax) = ?
A. A
B. a E(x)
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C. x E(a)
D. Non of these
E(ax + b) = A E(x) + ?
A. (C)
B. E(x)
C. b E(a)
D. b
Total Area under the curve in probability of density function is ?
A. 0
B. -1
C. 1
D. Infinity
An events that contains the finite number point the sample space is called
?
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A. Finite
B. Random
C. Continuous
D. values
The probability of a save event is equal to ?
A. Two
B. Three
C. Four
D. One
when a three die rolled the sample space consists of ?
A. 6 outcomes
B. 24 outcomes
C. 216 outcomes
D. Non of these
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The probability of even/odd numbers when a fair die is rolled is ?
A. 1/6
B. 2/6
C. 1/36
D. 3/6
If two events can both occur at the same time then they are referred
as: ?
A. Dependent events
B. Mutually Exclusive events
C. Exclusive events
D. Independent events
A list of sample is called sample space?
A. Events
B. Subset
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C. Piont
D. Distinct
A experiment repeated number of time one by one is called ?
A. Random
B. Raw data
C. Introduce
D. Specified
All experiments have properties in common?
A. Four
B. Three
C. Two
D. One
The probability of drawing a diamond card out of 52 cards is ?
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A. 13/52
B. 1/2
C. 4/52
D. 0
The probability of drawing same number on two dice if two dice are thrown
?
A. 1/36
B. 6/36
C. 12/36
D. 18/36
The square bracket is an finite G. Series is obtained by formula ?
A. 1/1-rn
B. a/1-r
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C. a/1-rn
D. a/(1-r)n
The probability of getting exactly two heads when two balanced coins are toss
once_ ?
A. 1/4
B. 2/4
C. 3/4
D. 4/4
A coin is so weighted that P (T) = 2P(H) then P(H) is ?
A. 1/2
B. 1
C. 2/3
D. 1/3
If P(B/A)= 0.25 and P(A∩B) = 0.2 then P(A) will equal to ?
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A. 0.05
B. 0.75
C. 0.8
D. 0.45
If P(A∩B) =1/4 then P(AUB) is _?
A. 1/2
B. 1/3
C. 1/12
D. 3/8
A∩B means: ?
A. The elements of A or B
B. The elements of A and B
C. The elements A but not of B
D. None of these
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If ‘A’ denotes the males of a town and ‘B’ denotes the females of that town, then A and B
are: ?
A. Equal sets
B. Over lapping sets
C. Non- overlapping sets
D. None of these
If a card is chosen from a standard deck of cards, what is the probability of getting a diamond
(◆) or a club ( )?
A. 26/52=1/2
B. 13/52
C. 20/52
D. 12/52
A listing of the possible outcomes of an experiment and their corresponding probability is
called: ?
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A. Random Variable
B. Contingency table
C. Bayesian table
D. Probability distribution
E. Frequency distribution
In which approach to probability the outcomes are equally likely to occur ?
A. Classical Probability
B. Subjective Probability
C. Relative Frequency
D. Independent
If a card is chosen from a standard deck of cards, what is the probability of getting a five or a
seven ?
A. 4/52
B. 1/26
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C. 8/52
D. 1/169
The joint probability is ?
A. The likelihood of two events happening together
B. The likelihood of two events happening given that another event has already ha
C. Based on two mutually exclusive events
D. Also called Prior probability
In special rule of addition of probability, the events are Always:_ ?
A. Independent events
B. Mutually Exclusive events
C. Bayesian
D. Empirical
The collection of one or more outcomes from an experiment is called: ?
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A. Probability
B. Event
C. Random Variable
D. Z-Value
E. Random Experiment
Which of the following is not an example of a discrete probability distribution ?
A. The sale or purchase price of a house
B. The number of bedrooms in a house
C. Whether or no t a home has a swimming pool in it.
D. Non of these
A subset of the sample space is called ?
A. Sample point
B. Set
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C. Event
D. Space
Two event are said to be equally likely is ?
A. As any other
B. both event occurs
C. One occurs
D. not both occurs
A set of events is said to be independent if probability of head on tossing a coin is
?
A. 1/2
B. 2/3
C. 1
D. 3/4
If the occurrence of excludes the occurrence of the other is called ?
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A. Mutually exclusive
B. Exchaustive
C. Likely
D. Probability
Addition Law of probability for mutually exclusive event is equal ?
A. P(AUB)=P(A) + (B)
B. P(AUB) = P(A) + P(B) – P(A∩B)
C. P(A∩B) = P(A) + P(B) + P(A∩B)
D. P(A∩B) = P(A). P(B
If the events have same chance of occurrence they are called:_ ?
A. Equally likely events
B. Exhaustive events
C. Mutually Exhaustive events
D. dependent events
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The possibility of total outcome in a coin equal to ?
A. Fifty %
B. Twenty %
C. 60%
D. 30%
Events occurring together without affecting each other are called: _?
A. Dependent events
B. Independent events
C. Equally likely events
D. Mutually Exclusive events
are said to be exhaustive if they constitute the entire sample space?
A. Equally
B. Events
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C. Outcomes
D. Objects
The picture cards having in total fifty two cards is equal ?
A. 16
B. 24
C. 12
D. Non of these
If an event consists of only one sample point is called ?
A. Appeared
B. Exactly
C. Space
D. Elementary event
The probability of an event cannot be ?
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A. Positive
B. Zero
C. None of these
D. Negative
The probability of drawing a picture card out of 52 cards is : ?
A. 13/52
B. 12/52
C. 16/52
D. 3/52
The probability of drawing an even number in a toss of a balanced die ?
A. 1/6
B. 2/6
C. 3/6
D. 6/6
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A box containing 12 balls of color 6 red and 6 white. A ball of white selected ball finds the
probability of white ?
A. 7/12
B. 6/12
C. 12/12
D. 4/12
A fair coin toss the total events in sample space equal ?
A. 7
B. 16
C. 36
D. 6
The probability that the sum is odd if two dice are thrown: ?
A. 18/36
B. 9/36
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C. 6/36
D. 12/36
The probability of getting exactly three tails when three balanced coins are tossed once
?
A. 1/8
B. 2/8
C. 5/8
D. 7/8
The probability of getting at least one head when two balance coins are tossed once
?
A. 1/4
B. 2/4
C. 3/4
D. 4/4
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If P(A/B)=1/4 and P(A∩B) =1/5 then P(B) is ?
A. 4/5
B. 1/20
C. 0
D. 1/9
If in a coin P(H) = 2P(T) then prob. of head is ?
A. 1/3
B. 2/3
C. 1/2
D. 0
The product of first ‘n’ natural numbers is ?
A. 1.2.3.4,………
B. 1.2.3……(n-2) (n-1) (n)
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C. n. (n-1) (n-2)…………..3.2.1.0
D. None of these
5C5 is equal to ?
A. 5
B. 5×5
C. 1
D. None of these
. If the occurrence of one event means that another cannot happen, then the events are
?
A. Independent
B. Mutually Exclusive
C. Bayesian
D. Empirical
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if you roll a pair of dice, what is the probability that (at least) one of the dice is a 4 or the sum
of the dice is 7 ?
A. 4/36
B. 13/36
C. 21/36
D. 15/36
The special rule of multiplication of probability, the events must be ?
A. Independent
B. Mutually exclusive
C. Bayesian
D. Empirical
Which of the following is not a correct statement about a Probability ?
A. It must have a value between 0 and 1
B. It can be reported as a decimal or a fraction
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C. A value near 0 means that the event is not likely to occur/happens
D. It is the collection of several experiment
In a Poisson probability distribution ?
A. The mean and variance of the distribution are same (equal)
B. The probability of success is always greater than 5
C. The number of trials is always less than 5
D. it always contains a contingency table
Least square regression line always passes through ?
A. (x,y)
B. (X,Y)
C. (X,Z)
D. x/y
The regression co-efficient are origin?
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A. Dependent
B. Independent
C. Scale
D. Both
When the two regression lines coincide there r is ?
A. Zero
B. Less than zero
C. More than zero
D. Great
Regression co-efficient is denoted by ?
A. by
B. byx
C. bzx
D. m
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Correlation coefficient lies between ?
A. 0 ≤ r ≤ 1
B. 0 ≤ r ≤ -1
C. -1 ≤ r ≤ 1
D. 1 ≤ r ≤ 0
Which of the following can never be taken as coefficient of correlation is ?
A. -99
B. .99
C. 0
D. √3
If r, between u = x and y = -x is _?
A. +1
B. -1
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C. 0
D. Non of these
The two regression co-efficient always have the sign?
A. Different
B. Same
C. None of these
D. +ve
A model is linear if it is linear in the dependent variable and also in ?
A. Parameter
B. Independent variable
C. Error term
D. Non of these
If y = 2 + 6x then value of y intercept is ?

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A. 6
B. 2
C. 0
D. None
In correlation, both variables are ?
A. Random
B. Fixed
C. Non-random
D. Experimental
If x = 3 then value of regression co-efficient of X or Y is ?
A. (3)
B. (0)
C. -3
D. -4
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Correlation is of regression coefficients?
A. A.M.
B. G.M.
C. M.D.
D. H.M.
Correlation coefficient is of origin and unit of measurement?
A. Origin
B. Dependence
C. Independence
D. None
In x = 2 6y the value of y are increasing by one unit then values of x are?
A. Increasing by 6
B. Decreasing by 6
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with respect to x and y?
C. No change
D. Non of these
Correlation coefficient is
A. +vely
B. Non-normal
C. Symmetrical
D. Skewed
?
If bxy = -.8 by x = 1.2 then value of r is
A. √.96
B. √-.96
C. 0
D. None of these
If bxy = byx = r then ?
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A. 6x < 6y
B. 6y < 6x
C. 6x = 6y
D. Non of These
In r x c table for test of Independence the degree of freedom is ?
A. r + c
B. rc
C. ι r – c ι
D. (r -1) (c -1)
The table representing two attributes is called ?
A. Random table
B. Contingency table
C. Dichotomy table
D. Chi-square table
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0314-4646739 0336-4646739
To cut a population into three classes is called ?
A. Dichotomy
B. Capital
C. Tracheotomy
D. Attribute
γxy is always equal to ?
A. γyx
B. -γyx
C. γx
D. γo2
Richness is not a ?
A. Constant
B. Discreade
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C. Variable
D. Continuous
Attributes are if they have some relation?
A. Disassociation
B. In consistent
C. Associated
D. None of these
In perfect association the value of coefficient of association is ?
A. (0)
B. +1
C. -1
D. non of these
Two attributes are associated if expected frequency is ?
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A. Less than observed
B. Greater than observed
C. Equal to observed
D. None of these
If x and y are Independent to each other the coefficient of correlation is ?
A. -1
B. +1
C. .6
D. 0
(A β C) is a frequency of attributes of order _?
A. 3
B. (2)
C. 1
D
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If (AB) >(A) (B)/n then A and B are?
A. Independent
B. Associated
C. Dis-associated
D. None of these
If the sampled population has a normal distribution, when is the sampling distribution of the
sample mean X also a normal distribution ?
A. Only when the sample size is at least 100.
B. Only when the sample size is smaller than 30
C. Always
D. Only when the sample size is at least 30.
In the sampling without replacement a sampling unit can be selected ?
A. Only Once
B. More than once
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C. Less than once
D. None of these
The smallest individuals which constitute the entire population are called
?
A. Sampling frame
B. Sampling units
C. Sample pop
D. Sample design
There are probability sampling?
A. Four
B. Six
C. Three
D. Seven
In probability sampling each sampling unit has some ?
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A. Unknown
B. Large
C. Small
D. Know
Standard deviation of the sampling distribution of a statistics is called ?
A. Serious error
B. Dispersion
C. Standard error
D. Difference
In w.o.r 2σx= ?
A. 26/√n√N – n/N – 1
B. σ/√n√N – n/N – 1
C. 26/√n N – n/N – 1
D. 26/√n
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The difference between statistics and parameter is called: _?
A. Bias
B. Standard
C. Sampling error
D. both (a) and (b)
Random samples of size 17 are from a population that has 200 elements, a mean of 36, and a
standard deviation of 8. which of the following best describes the from of the sampling
distribution of the sample mean for this situation ?
A.Approximately normal because the sample size is small relative to the population
size
B. Approximately normal because of the central limit theorem
C. Exactly
D. None of these alternatives is correct
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A sample of 24 observations is taken from a population that has 150 elements. The sampling
distribution of is ?
A. Approximately normal because is always approximately normally distributed
B.Approximately normal because the sample size is large in comparsion to the
population size
C. Approximately normal because of the central limit theorem
D. Normal if the population is normally distributed
The sampling error is the ?
A. Same as the standard error of the mean
B.Difference between the value of the sample mean and the value of the population
mean
C. Error caused by selecting a bad sample
D. Standard deviation multiplied by the sample size
A sample estimate is used to describe a characteristic of a ?
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A. Sample
B. Data
C. Population
D. None
Which of the following is impossible in sampling ?
A. Destructive tests
B. Heterogeneous data
C. To make voters lists
D. None of these
For making voters lists in Pakistan we need ?
A. Simple random sampling
B. Systematic sampling
C. Quota sampling
D. Census
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If in a sampling distribution of X the sample size is 25, what assumption must hold for the
sampling distribution of X to be normal ?
A. Population distribution is normal
B. μ1 = μx
C. Population distribution is uniform
D. σx = σx /√n
Non-sample errors are reduced by: ?
A. Increasing the sample size
B. Reduced the amount of data
C. Decreasing the sample standard deviation
D. None of these
Sampling error can reduced by ?
A. Non-random sampling
B. Increasing the population
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C. Decreasing the sample size
D. Increasing the sample size
The process of selecting sample from the population is called ?
A. Sampling process
B. Sampling unit
C. Sampling
D. Size
N – n/N -1 is called population?
A. Group
B. Finite
C. Un-finite
D. Correction
Probability distribution of a statistics is called ?
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A. Sampling
B. Parameter
C. Data
D. Sampling distribution
Selection of s by the students to solve a paper is ?
A. Random sampling
B. Non-random sampling
C. Prob.Sampling
D. Sampling with replacement
A sampling distribution is the probability distribution for which one of the
following _?
A. A sample
B. A sample statistic
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C. A population
D. A population parameter
Non-random sampling is also called ?
A. Biased sampling
B. Non-prob.sampling
C. Less than sampling
D. Representative sampling
To purchase the fruit, we use the sampling?
A. Systematic
B. Cluster
C. Stratified
D. Judgment
A list of sampling is called sampling frame?
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A. Point
B. w.r.m
C. w.o.r
D. unit
In sampling with replacement be t a sampling unit can selected ?
A. Only once
B. More than once
C. Less than once
D. None
Sampling errors are reduced by: ?
A. Increasing the sample size
B. Decreasing the sample size
C. Increasing population s.d.
D. None of these
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If we increase the sample size, it means that it: ?
A. Increases the Standard error
B. Decreases the Standard error
C. Decreases the Standard error
D. Both (a) and (b)
For a population consisting of 4 members, a sample of size ‘2’ is taken replacement, then the
number of all the possible samples are?
A. 4
B. 8
C. 16
D. 32
The process of dividing a heterogeneous ?
A. Random digit
B. Stratification
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C. Random Sampling
D. Cluster
Convenience sampling is an example of ?
A. Probabilistic sampling
B. Stratified sampling
C. No probabilistic sampling
D. Cluster sampling
For a population with any distribution, the form of the sampling distribution of the sample
mean is ?
A. Sometimes normal for all sample sizes
B. Sometimes normal for large sample sizes
C. Always normal for all sample sizes
D. Always normal for large sample sizes
The standard deviation of sampling distribution of a statistics is _ ?
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A. Standard error of statistics
B. Sampling error of statistics
C. Sampling distribution of statistics
D. None of these
A sample of 92 observations is taken from an infinite population. The sampling distribution of
is approximately ?
A. Normal because is always approximately normally distributed
B. Normal because the sample size is small in comparison to the population size
C. Normal because of the central limit theorem
D. None of these alternatives is correct.
A is the specific value of the statistic used to estimate the population parameter?
A. Point estimator
B. C.I.
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C. Estimator
D. None of these
Since E(X) X is said to be unbiased estimator of the population mean?
A. Q
B. X
C. Ux
D. u
Sampling Error decrease by the sample size?
A. Increase
B. Decrease
C. Sampling
D. Population
is a value of sample statistics?
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A. Estimate
B. Estimator
C. Probability
D. Numerical
The Estimation and testing of hypothesis are main branches of ?
A. Sampling
B. Probability distribution
C. Regression
D. Statistical Inference
95% confidence limits for P are ?
A. P±2.18√p2q2/n
B. P±1.65(pq/n)
C. P±1.96 p2q2/√n
D. P±1.96√p2q2/n
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The hypothesis which is being tested is called ?
A. Composite hypothesis
B. Alternative hypothesis
C. Null hypothesis
D. Simple hypothesis
Type II error is committed when the null hypothesis is _?
A. Rejected when it is true
B. Rejected when it is false
C. Accepted when it is true
D. Accepted when it is false
Which of the following cannot be Ho ?
A. Q ≤ Qo
B. Q ≥ Qo
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C. Q = Qo
D. Q ≠ Qo
If Ho is stated as Q = Qo< the alternate hypothesis in general stated _?
A. Q Qo
C. Q ≠ Qo
D. None of these
The first and starting point in test Hypothesis is ?
A. stating H1
B. stating Ho
C. L of significance
D. Test statistics
Criteria to check a point estimator to be good are ?
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A. Consistency
B. All Above
C. Unbiasedness
D. Efficiency
Consistency of an estimator can be checked by comparing ?
B. Mean
C. mean Square Error
D. Variance
Herbicide A has been used for years in order to kill a particular type of weed. An experiment is
to be conducted in order to see whether a new herbicide, Herbicide B, is more effective than
Herbicide A. Herbicide A will continue to be used unless there is sufficient evidence that
Herbicide B is more effective. The alternative hypothesis in this problem is ?
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A. Herbicide A is more effective than Herbicide B
B. Herbicide A is not more effective than Herbicide B
C. Herbicide B is more effective than Herbicide A
D. Herbicide B is not more effective than Herbicide A
Which of the following is an assumption underlying the use of the t-distribution ?
A. The sample are drawn from a normally distributed population.
B. The variance of the population is known
C. All above
D. s (sample standard deviation) is an unbiased estimate of the population variance.
The t distribution are ?
A. Symmetrical
B. None of these
C. Same as Normal Curve
D. Skewed
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Which of the following is a true statement for comparing the t distribution with standard
normal ?
A.Greater the degree of freedom, the more the t-distribution resembles the
standard normal distribution
B. The Normal Curve is symmetrical whereas the t-distribution are slightly skewed.
C.The proportion of area beyond a specific value of “t” is less than the proportion of
normal curve
D. Non of these
The Mann-Whitney U test is preferred to a t-test when ?
A. Sample are dependent
B. The assumption of normality is not met
C. Sample sizes are small
D. Data are paired
The sign test assumes that the _?
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A. Samples are independent
B. Samples have same mean
C. Sample are dependent
D. The Wilcoxon Signed Rank test is used
Three brands of coffee are rated for tasted on a scale of 1 to 10. Six persons are asked to rate
each brand so that there is a total of 18 observations.The appropriate test to tasted equally
good is _ _?
A. One way analysis of variance (ANOVA)
B. Spearman Rank difference
C. Wilcoxon Rank-Sum test
D. Kruskal-Wallis test
To perform a Runs test for randomness the data must be _?
A. Divided into at least two classifications
B. Divided into exactly two classifications
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C. Quantitative
D. Qualitative
The Spearman Rank-Correlation test requires that the ?
A. Data must be measured on the same scale
B. Data should be of ordinal scale at least
C. Data must be distribution at least approximately as a t-distribution
D. Data must be from two independent samples
In a Wilcoxon Rank-Sum test ?
A. Ties within one sample may affect the decision
B. Ties always affect the decision
C. Ties never affect the decision
D. Ties between the two sample may affect the decision
When using the sign test, if two scores are tied, then ?
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A. We count them
B. We discard them
C. We depends upon the scores
D. non of these
Wilcoxon Rank-Sum test can be of ?
A. Lower tailed
B. Upper tailed
C. Either of the above
Which of the following test use Rank Sums ?
A. Kruskal-Wallis and Wilcoxon tests
B. Runs test
C. Chi-Square and sign test
D. F test
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if f(x1,x2,…xn;θ)=g(θˆ;θ)h(x1,x2,….,xn), then θˆ is ?
A. Consistent
B. Sufficient
C. Efficient
D. Unbiased
if Var(θˆ)→0 as n → 0, then θˆ is said to be ?
A. Sufficient
B. Efficient
C. Unbiased
D. Consistent
Let X1,X2,…Xn be a random sample from the density f(x;(θ), where θ may be vector. If the
conditional distribution of X1,X2,…Xn given S=s does not depend on θ for any value of s of S,
then statistic is called?
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A. Minimal sufficient statistic
B. Sufficient statistic
C. Efficient
D. Minimax statistics
Let Z1,Z2,….Zn be independent and identically distributedrandom variable, satisfying E[ι Zt
ι]<∞. Let N be an integer valued random variable whose value n depends only on the values of
the first n Z¡'s. Suppose E(N)< ∞, then E(Z1,Z2,….Zn)=E(N)E(Z) is called ?
A. Independence Equation
B. Sequential Probability Likelihood Equation
C. Neyman Pearson Lemma
D. Wald’s Equation
For a biased estimator θˆ of θ, which one is correct ?
A. MSE(θˆ)=SD(θˆ)+Bias
B. MSE(θˆ)=Var(θˆ)+Bias2
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C. MSE(θˆ)=SD(θˆ)+Bias2
D. MSE(θˆ)=Var(θˆ)+Bias
If the conditional distribution of X1,X2,…..Xn given S=s, does not depends on θ, for any value
of S=s the statistics S=s(X1,X2,…..Xn) is called _?
A. Unbiased
B. Sufficient
C. Consistent
D. Efficient
A test is said to be most powerful test of size α, if ?
A. Among all other test of size α or less it has the largest power
B. Among all other test of size α or greater it has the largest 1 – α
C. Among all other test of size α or greater it has the smallest power
D. Among all other test of size α or greater it has the largest β
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for two estimators T1=t1(X1,X2,….Xn) and T1=t1(X1,X2,….Xn) then estimators t1 is defined to
be Rt1(θ)≤Rt2(θ) for all θ in Θ ?
A. Consistent estimator
B. Admissible estimator
C. Sufficient estimator
D. Minimax estimator
if Var(T2) ?
A. Efficient
B. Sufficient
C. Unbiased
D. Consistent
If E(θˆ)=θ, then θˆ is said to be _?
A. Unbiased
B. Consistent
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C. Sufficient
D. Efficient
Let X1,X2,……,Xn be a random sample from a density,,,, f(x ι θ) where θ is a value of the
random variable Θwith known density gΘ(θ) Then the estimator ∏(θ) with…/ respect to the
prior gΘ(θ) is define as E[∏(θ)ιX1,X2,…..,Xn] is called?
A. Posterior Bay’s estimator
B. Minimax estimator
C. Bay’s estimator
D. Sufficient estimator
An estimator Q is an unbiased estimator of the population parameter Q if
?
A. E(x) = µ
B. E(Q) =Q
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C. E(Q) =Q
D. E(P) = P
Sample proportion P is _ estimator?
A. Biased
B. Parameter
C. Unbiased
D. None of these
Sample variance S2 is unbiased estimator of population variance 26 because
?
A. E(S2) = s2
B. E(u) = X
C. E(P) = P
D. Ux = u
x=40 is estimator of ?
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A. (U)
B. 6
C. Ux
D. 6/√n
is an estimate expressed by a single value?
A. C.I.
B. Point estimator
C. Parameter
D. Point estimate
is the process of using sample information to reach?
A. Population
B. Biased
C. Unbiased
D. Increase
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The minimum variance unbiased estimator of the population mean is ?
A. 6/√n
B. S/√n
C. S2/n
D. 6x/√n
95% confidence limits u are ?
A. x±1.65 6/√n
B. u±1.95 S/√n
C. x±1.96 6/√n
D. ±1.96 6/√n
E(x1 – x2)= ?
A. ux – x2
B. u1 – u2
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C. 6x – x2
D. 6×2 – x2
Which of the following is simple hypothesis ?
A. u = 20
B. u ≠ 20
C. u 20
If n = 400 and P=.69 then 90% C.I for P is ?
A. 652 and . 728
B. .314 and .652
C. .798 and .745
D. None of these
The level of significance is denoted by ?
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A. 1 – ∞
B. β
C. ∞
D. 1 – β
The values that separate the region of rejection and acceptance region are called
?
A. Critical value
B. Confidence limits
C. Confidence boundaries
D. None of these
Power of test is denoted by ?
A. β
B. α
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C. (1 – α )
D. (1 – β)
1 – α is the probability of ?
A. Acceptance Region
B. Type-I error
C. Type-II Error
D. Rejection Region
Parameter is a quantity?
A. Constant
B. Variable
C. All of above
D. Non of these
If we reject the null hypothesis, we might be making ?
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A. Unpredictable
B. A correct Decision
C. Type-II Error
D. Type-Error
Analysis of Variance (ANOVA) is a test for equally of ?
A. Variances
B. Proportions
C. Only two parameters
D. Means
A quantity obtained by applying certain rule or formula is known as ?
A. Estimate
B. Test Statistics
C. Estimation
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D. Sample
E. Estimator
For t distribution, increasing the sample size, the affect will be on ?
A. Standard Error of the Means
B. The t-ratio
C. Degrees of Freedom
D. All Above
condition for applying Central Limit Theorem (CLT) which approximate the sampling
distribution of the mean with a normal distribution is ?
A. n > 30
B. N(1 – p) > 5
C. 2 n 5
E. N < 30
what is the probability of a type II error when α=0.05 ?
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A. 0.025
B. 0.95
C. 0.05
D. Cannot be determined without more information
The critical value of a test statistic is determined from ?
A. The sampling distribution of the statistics assuming Null Hypothesis
B. calculations based on many actual repetitions of the same Experiment
C. The sampling distribution of the statistic assuming Alternative Hypothesis.
D. Non of these
In testing for the difference between two populations, it is possible to use ?
A. The Wilcoxon Rank-Sum test
B. The Sign test
C. None of the above
D. Either of the above
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The Runs test results in rejecting the null hypothesis of randomness when ?
A. There is an unusually large number of runs
B. There is an unusually small number of runs
C. None of these
D. Either of the above
Comparing the times to failure of radar transponders made by firms A, B, and C based on an
airline’s sample experience with the three types of instruments one may use_ ?
A. Kolmogorov-Smirnor test
B. Wilcoxon Rank-Sum test
C. Spearman Rank Correlation test
D. Kruskal-Wallis test
The Wilcoxon, Rank-Sum test used to compares ?
A. Any number of populations
B. A sample mean to the population mean
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C. Two populations
D. Three populations
Which of the following test must be two-sided ?
A. Sign test
B. Wilcoxon Signed Rank
C. Kruskal-Wallis
D. Runs test
Which of the following test is most likely assessing this null hypothesis: Ho The number of
violations per apartment in the population of all city apartments is binomially distributed with
a probability of success in any one trial of P=0.3 dd ?
A. The Mann-Whitney test
B. The Kruskal-Wallis test
C. The Wilcoxon Signed Rank test
D. The Kolmogorove-Simirnor test
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When testing for randomness, we can use ?
A. Sign test
B. None of these
C. Runs test
D. D Mann-Whitney U test
The non parametric equivalent of an unpaired samples t-test ?
A. Kruskal Wallis Test
B. Mann-Whitney U test
C. Wilcoxon signed rank test
D. Sign test
Let X1,X2,……,Xn be a random sample from a density,,,, f(x ι θ) where θ is a value of the
random variable Θwith known density gΘ(θ) Then the estimator ∏(θ) with…/ respect to the
prior gΘ(θ) is define as E[∏(θ)ιX1,X2,…..,Xn] is called?
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A. Posterior Bay’s estimator
B. Minimax estimator
C. Bay’s estimator
D. Sufficient estimator
In binomial distribution the probability of success remains from trial to trial?
A. Constant
B. Varies
C. Four
D. Probability
A binomial random variable can assume values from to n?
A. 6
B. 3
C. 2
D. 0
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In the binomial experiment, the outcomes of each trial maybe classified into
?
A. Success
B. Failure
C. Success or Failure
D. None of these
In binomial experiment, the successive trials are ?
A. Dependent
B. independent
C. Related
D. constant
In binomial experiment successive trials are _?
A. Dependent
B. Independent
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C. May be inependent or dependent
D. None of these
When X denotes the number of success in binomial experiment, it is called
?
A. Random variable
B. Binomial random variable
C. Continuous random variable
D. Both (b) and (c) but not (a)
In a binomial distribution the probability of changes from trial to trial?
A. Failure
B. Experiment
C. Success
D. Out come
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The hypergeometric probability distribution is used rather than the binomial or Poisson when
the sampling is performed ?
A. With replacement
B. With out replacement from an infinite population
C. With out replacement from a finite population
D. With replacement from a finite population
Binomial distribution is symmetrical when P= ?
A. 1/q
B. 1
C. q
D. 2q
Binomial distribution is used when n is ?
A. Large
B. Small
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C. Zero
D. Normal
Binomial distribution is used when _ is large?
A. nP
B. nq
C. p
D. n
If u = 5 and S.D. = 2.5 then Binomial distribution are ?
A. Unequal
B. Wrong
C. Fair
D. None of these
In a binomial distribution mean and variance is ?
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A. Variance > mean
B. Mean < variance
C. Variance ≠ mean
D. None of these
Which of the following is not a requirement for binomial distribution ?
A. Constant Probability of Success
B. Only two possible outcomes
C. A fixed number of trials
D. Equally likely outcomes
If then the distribution is positively skewed?
A. p < q
B. q/p
C. p > q
D. p > 1/2
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For a binomial distribution?
A. n must assume a number between 1 and 20 or 25
B. p must be a multiple of 10
C. There must be at least 3 possible outcomes
D. None of these
If a Binomial experiment is repeated ‘N’ times then binomial frequency distribution is.
?
A. N.{nx}px qn-x
B. N p q
C. N.{n/x}px qn-x
D. N.{n/x}p qn-x
If 5 dice are rolled 96 times then N. = ?
A. 5
B. 96
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C. 5/96
D. 96/5
The binomial distribution is positively skewed when: ?
A. p > q
B. p < q
C. p = q
D. both (a) and (b
If in binomial distribution p ≠ q, the distribution is: ?
A. Positively skewed
B. Negative skewed
C. May be positive skewed or negative skewed.
D. None of these
The sum of p and q is always: ?
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A. 0
B. 2
C. 1
D. None of these
What is the variance of binomial distribution ?
A. n p
B. np (1 – p)
C. np/q
D. nq/p
Variance of binomial distribution is always: ?
A. Less than mean
B. Greater than mean
C. Equal to mean
D. Less than equal to mean
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In a binomial distribution, n = 20 and p = 3/5, then variance of this distribution
?
A. 60
B. 12
C. 4.8
D. 0
if in a binomial probability distribution mean and variance are 6 and 2.4 respectively, then the
parameters of this distribution are: ?
A. n = 10, p = 6/10
B. n = 50, p = 6/50
C. n = 10, p = 3/5
D. n = 10, p = 2/5
Which of the following is not a condition of the binomial distribution ?
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A. Only 2 possible outcomes
B. Have constant probability
C. Must have at least 3 trials
D. Trials must be independent
The successive trials are with replacement in: ?
A. Hpergeometric distribution
B. Binomial distribution
C. Geometric distribution
D. None of these
Binomial distribution is symmetrical when: ?
A. p = q
B. p > q
C. p > q
D. np > npq
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The variance of binomial distribution is always: ?
A. Less than mean
B. Equal to mean
C. Greater than mean
D. Equal to standard deviation
E. None of these
Binomial distribution has parameters:_ ?
A. Three
B. Two
C. One
D. Four
E. None
Binomial distribution is negatively skewed when:_ ?
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A. p=0
B. p>1/2
C. p=1/2
D. p=1/3
The mean, median and mode for binomial distribution will be equal when: ?
A. p= 0.5
B. P 0.5
D. p = 1
E. None of these
If in a binomial distribution n = 1 then E(X) is: ?
A. q
B. p
C. 0
D. 1
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A random variable X has binomial distribution with n = 10 and p = 0.3 then variance of X
is: ?
A. 10
B. 12
C. 2.1
D. 21
E. None
In binomial distribution n=6 and p=0.9, then the value of _?
A. P(X=7) is
B. One
C. Less than zero
D. Zero
E. More than zero
Successive trials in binomial distribution are: ?
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A. Dependent
B. Independent
C. Equally Likely
D. Mutually exclusive
E. Non
Binomial distribution has parameter?
A. 4
B. 3
C. 2
D. 6
Binomial distribution is symmetrical when P= ?
A. n
B. x
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0314-4646739 0336-4646739 0332-4646739
C. q
D. 1 – P
In binomial experiment, the probability of success is denoted by _?
A. P
B. q
C. P
D. 1 -P
The mean of a binomial distribution is always: ?
A. Equal to variance
B. Less than variance
C. Greater than varince
D. None of these
Mean of the binomial distribution is ?

A. Pq
B. nP
C. xm
D. Non of these
The mean and variance of binomial distribution are ?
A. Unequal
B. Equal
C. Symmetrical
D. None
In binomial distribution with trials mean is np and variance is npq?
A. Dependent
B. Independent
C. Linear
D. Equal
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In binomial experiment, the experiment is repeated ?
A. n; fixed number of times
B. a large number times
C. n; where n < 0
D. n = 100
Binomial distribution is positively skewed when ?
A. p > q
B. P = q
C. p < q
D. P/q
(q + p) has variance is ?
A. 6 pq
B. npq
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C. 7 pq
D. 3 pq
If mean and variance are not equal then distribution ?
A. None
B. Symmetrical
C. Skewed
D. Equal
In a binomial distribution mean and variance is ?
A. Variance > mean
B. Mean < variance
C. Variance ≠ mean
D. None of these
Binomial distribution ranges from ?
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A. 1 to n
B. 0 to n
C. 1 to ∞
D. 0 to ∞
If p= 0.1 and n = 400 then mean ?
A. 60
B. 30
C. 20
D. 40
The experiment is repeated a number of times?
A. Times
B. Fixed
C. Expansion
D. Trial
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There are parameter in Binomial distribution?
A. n, q
B. n, p, q
C. q, p
D. n, p
Binomial word discovered at the end of ?
A. 14th century
B. 12th century
C. 10th century
D. 17th century
Binomial probability distribution is denoted by b(x ; n, p), is defined as ?
A. {nx}px qn-x
B. {nx}px(1 – P)x-n
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C. nCxpnqnx
D. {nx}p(1 – P)x
What is the mean of binomial distribution ?
A. X
B. n x p
C. n(1 – 1)
D. ∑fx/∑f
The binomial distribution is symmetrical when: ?
A. P > q
B. P = 1/2
C. Probability of success & probability of failure are equal
D. Both (b) & (c) but not (a)
Which of the following case is true for hyper geometric distribution ?
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A. Probability remains constant for all the trials.
B. Probability changes from trial to trial
C. Successive trial are dependent
D. Both (b) & (c) but not (a)
In a binomial distribution, n = 10 p= 3/5, its mean is: ?
A. 6
B. 1
C. 2/5
D. None of these
For a binomial distribution with n = 15 as p changes from. 50 toward. 05 the distribution
will ?
A. Become more positively skewed
B. Become more negatively skewed
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C. Become symmetrical
D. All of the above.
When ‘n’ becomes very large, binomial distribution tends to ?
A. Poisson dist
B. Standard dist
C. Normal dist
D. Hyper-geometric distribution
If mean of the binomial probability distribution is 4.8, then variance of this distribution is
: ?
A. -2.3
B. 5.3
C. -4.8
D. 2.3
The mean and the variance are equal in ?
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A. All probability distribution
B. The hypergeometric distribution
C. The binomial distribution
D. The Poisson distribution
The probability of success changes from trial to trial in: _ ?
A. Binomial distribution
B. Geometric distribution
C. Sampling distribution
D. Hypergeometrical distribution
The mean of binomial distribution is: ?
A. npq
B. np
C. √npq
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D. √np
E. nq—√
In a binomial probability distribution it is impossible to find ?
A. P(X < 0)
B. P(X = 0)
C. P(X > 0)
D. p(0 ≤ X≤ n)
Hypergeometric distribution has parameter:_ ?
A. 2
B. 1
C. 3
D. 4
E. No
Which of the following is not the property of binomial distribution ?
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A. n is fixed
B. Has two outcomes
C. Trials are independent
D. Probability of success varies from trial to trial
The mean of hypergeometric distribution is: ?
A. Nk/N
B. N-k/n
C. nN/k
D. n+k/N
In hypergeometric distribution, the trial are: ?
A. Independent
B. Dependent
C. Collectively Exhaustive
D. None
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In which distribution successive trials are without replacement:_ ?
A. Hypergeometric distribution
B. Binomial distribution
C. Poisson distribution
D. Geometric distribution
Each trial in Binomial distribution has: ?
A. One Outcome
B. Two Outcome
C. Three Outcome
D. Four Outcome
The index numbers are used to measure seasonal and cyclical variations in _?
A. Commodities
B. Time Series
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C. Whole sale
D. Realtives
An Index Number calculated for more than one items is called ?
A. Sensitive Price Index number
B. Consumer Index Number
C. Simple Aggregation 1. Number
D. Chain Indices
Ratio between given year and base year is called in percentage?
A. Price relative
B. Link relative
C. Retail prices
D. None of these
Weighted Index number can be classified into categories?
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A. Four
B. Three
C. Five
D. Two
Price in proceeding year used in the method is called ?
A. Fixed Method
B. Chain Method
C. Aggregation Method
D. Volume
Measure the change in quantity of goods are called ?
A. Simple 1. No.
B. Aggregative 1. No.
C. Appropriate
D. Quantity Index Number
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1. Nos. is a for measuring changes in a variable or a group of related variables?
A. variable
B. Region of goods
C. Device
D. Cost
Index Number is an important role in the field of Economic and ?
A. Science
B. Education
C. Intelligence
D. Business
Qon means _ for the given year?
A. Price
B. Commodity
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C. Quantity in current
D. Quantity Index
Volume Index in Marshall is ?
A. ∑Pn(Po + Pn)/∑Pn(Po + Pn)
B. ∑Pn(qo + qn)/∑Pn
C. ∑Pn(Po + Pn)/∑Pn(Po + Pn) x100
D. Non of these
In Chain base method, the base period is ?
A. Fixed
B. Constant
C. Change
D. None of these
Link relative = ?
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A. Pn/pn-1 x100
B. Pn/Po x10
C. Pn/Po x100
D. None of these
Paasche’s Index number is ?
A. ∑pnqo/∑poqo
B. ∑pnqo/∑pnqo x100
C. ∑pnqn/∑poqo
D. ∑pnqn/∑poqn x100
Which of the formula is used in chain indices: ?
A. ∑pn/∑po x100
B. pn/po x100
C. pn/pn-1 x100
D. Both (a) and (b) but not (c)
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The index number of base period is always: _?
A. 100
B. 200
C. The price of that year
D. None of these
The ratio of a new price to the base year price is called the ?
A. Price decrease
B. Price absolute
C. Price increase
D. Price relative
A simple aggregate price index ?
A. Ignores relative quantities
B. Compares relative quantities to relative prices
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C. Compares absolute prices to absolute quantities
D. Compares relative quantities
The Laspeyres and Paasche index are examples of ?
A. Aggregate index numbers
B. Weighted index numbers
C. Weighted price index only
D. Weighted quantity index only
The formula ∑poqn/∑poqo x100 is used to calculate ?
A. The Laspeyres price index
B. The Paasche quantity index
C. The Laspeyres quantity index
D. The Paasche price index
A scaling factor is used to ?
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A. Change a simple index to a weight index
B. Convert the Paasche index to a Laspeyres index
C. Change the base year
D. change an aggregate index to a weighted index
All Index numbers are not suitable for all ?
A. Kind
B. Chain relative
C. Purpose
D. Price
Consumer price Index Number also called is designed to measure changes?
A. Cost Living Index number
B. Whole Sale Index number
C. weighted Index Number
D. Consumer Index Number
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0314-4646739 0336-4646739
An Index number of an average quality of wheat in Lahore_ Index?
A. Volume Index Number
B. value Index Number
C. Quantity Index Number
D. Weighted Index Number
G.M. between is called to be Fisher’s Index Number?
A. Paasche’s Index Number
B. Marshall and Laspeyr’es
C. Laspeyre’s and Paasche’s
D. Fisher and Paasche’s
Average calculated used in index number by method?
A. Three
B. Two
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C. Four
D. One
The object of Index number also determines its ?
A. Index Number
B. Special purpose
C. Reliable
D. Scope
An Index number which measure the change of a is called Aggregative 1. No?
A. Industrial activity
B. Retail price
C. Cost of living
D. Goods consumed
Single number which shows changes in a phenomenon is called an Index
Number?
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A. Overall
B. Same
C. Variation
D. Capable
Link relative = ?
A. Pn/Po x 100
B. Pn/Po x 100
C. Pn/ Pn-1 x100
D. Pn/P1 x 100
The weighty system changed with ?
A. Yearly
B. Basely
C. Timely
D. Averagely
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The Index number are used to measure seasonal and cyclical variations in ?
A. Wholesale
B. Relatives
C. commodities
D. Time series
Volume index in Marshall is ?
A. ∑pn(Po + Pn)/ ∑pn (Po + Pn)
B. ∑qn(qo + qn)/∑qn(po + pn) x100
C. ∑pn(qo + qn)/∑pn
D. ∑qn(Po + Pn)/ ∑qo (Po + Pn) x100
Base year quantities are used as weights in _?
A. Laspeyre’s index
B. Paasche’s index
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C. Fisher’s index
D. None of these
Fisher’s ideal index number is also obtained by ?
A. Taking A.M. of Laspeyre’s and Paasche’s index
B. Taking G.M. of Laspeyre’s and Paasche’s index
C. Both (a) and (b)
D. None of these
An index number is used ?
A. To measure changes in quantity
B. To measure changes in price
C. To measure changes in a variable over time
D. To measure changes in demand
A simple aggregate quantity index is used to _?
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A. Measure the change in quantity of product
B. Measure the overall change in price of a range of products
C. Measure the overall change in quantity of range of product.
D. Measure the change in price of a product
This index measure the change from month to month in the cost of a representative ‘basket’
of goods and services of the type bought by a typical household?
A. Laspeyres Price Index
B. Financial time Index
C. Paasche Price Index
D. Retail Price Index
The Laspeyres price index ?
A. Regards the base year quantities as fixed
B. Regards the base year price as fixed
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C. Regards the current year quantities as fixed
D. non of these
The formula ∑pnqn/poqn x100 is used to calculate?
A. The Laspeyres price index
B. The Paasche price index
C. The Paasche quantity index
D. The Laspeyres quantity index
In a symmetrical distribution mean, median and mode, ?
A. Positive
B. Greater
C. Less than
D. Coincide
The A.M. is greater than mode is equal to ?
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A. +vely
B. Skewness
C. Negatively
D. zero
Range of 5,5,5,5, is ?
A. 0
B. 5
C. 25
D. None of these
The degree to which numerical data tend to spread about an average value is
a ?
A. Range
B. variance
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C. Minimum
D. Dispersion
If y = bx + a the mean deviation of y is ?
A. S.D. of y
B. var (x)
C. S.D. of x
D. M.D.of x
Absolute sum of deviations is minimum from ?
A. Coefficient of variance
B. S.D. of x
C. Mean
D. Normal
Relative measure of skewness was introduced by ?
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A. Rowely
B. Lack
C. Karl Person
D. Mode
In grouped data, the range is the difference between ?
A. Two extreme class boundaries
B. Two extreme class frequency
C. Two extreme class limits
D. None of these
Mean deviation is equal to 4/5 of the manipulation?
A. Quartile deviation
B. Range
C. Standard deviation
D. Variance
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0314-4646739 0336-4646739
The correct variance is define as the ?
A. varies of data P2/6
B. S.D. of data h2/12
C. M.D. of data h2/6
D. Variance of data h2/12
Mean deviation is always ?
A. Equal to S.D.
B. More than S.D.
C. Less than S.D.
D. Negative
The S.D. and variance are of origine?
A. Multiplied
B. Variance
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C. Change
D. Independent
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