This document contains a statistics reviewer with multiple choice questions and answers about statistical concepts such as: - Levels of measurement (nominal, ordinal, interval, ratio) - Measures of central tendency (mean, median, mode) - Probability distributions and calculating expected values - The normal distribution and z-scores - Sampling methods (simple random sampling, stratified sampling) The questions cover topics like identifying different levels of measurement, calculating averages, interpreting empirical rules for the normal distribution, and defining random variables, probability distributions, and sampling techniques.

1. STATISTICS REVIEWER

2. Which of the following is a
nominal level of measurement?
a) Height
b) Weight
c) Gender
d) Temperature
Answer: c) Gender

3. Which of the following is an
example of an ordinal level of
measurement?
a) Age
b) Income
c) Rating
d) Temperature
Answer: c) Rating

4. Which of the following is an
example of an interval level of
measurement?
a) Number of siblings
b) Social security number
c) Year of birth
d) Fahrenheit temperature
Answer: d) Fahrenheit
temperature

5. Which of the following is an
example of a ratio level of
measurement?
a) Height
b) IQ score
c) Zip code
d) Favorite color
Answer: a) Height

6. Which level of measurement is
most commonly used in surveys?
a) Nominal
b) Ordinal
c) Interval
d) Ratio
Answer: a) Nominal

7. Which level of measurement is
used to classify data into mutually
exclusive categories?
a) Nominal
b) Ordinal
c) Interval
d) Ratio
Answer: a) Nominal

8. Which level of measurement is
used to classify data into mutually
exclusive categories?
a) Nominal
b) Ordinal
c) Interval
d) Ratio
Answer: a) Nominal

9. Which measure of central
tendency is the most commonly
used?
a) Mean
b) Median
c) Mode
d) Range
Answer: a) Mean

10. Which measure of central
tendency is not influenced by
extreme values?
a) Mean
b) Median
c) Mode
d) Range
Answer: b) Median

11. What is the median?
a) The value that occurs most frequently
in a data set
b) The middle value in a data set
c) The value that is halfway between the
minimum and maximum values in a data
set
d) The value that is closest to the
arithmetic mean in a data set
Answer: b) The middle value in a
dataset

12. What is the mode?
a) The value that occurs most frequently
in a dataset
b) The middle value in a dataset
c) The value that is halfway between the
minimum and maximum values in a
dataset
d) The value that is closest to the
arithmetic mean in a dataset
Answer: a) The value that occurs most
frequently in a dataset

13. What is the range?
a) The difference between the highest and
lowest values in a dataset
b) The average of the highest and lowest
values in a dataset
c) The value that occurs most frequently
in a dataset
d) The middle value in a dataset
Answer: a) The difference between the
highest and lowest values in a dataset

14. What is the difference between the sample
mean and the population mean?
a) There is no difference.
b) The sample mean is always higher than the
population mean.
c) The population mean is always higher than
the sample mean.
d) The sample mean is an estimate of the
population mean based on a subset of the
data.
Answer: d) The sample mean is an estimate
of the population mean based on a subset
of the data.

15. What is the standard deviation?
a) A measure of the average distance of each
value from the mean.
b) The difference between the highest and
lowest values in a dataset.
c) The number of standard errors the sample
mean is from the population mean.
d) The average of the highest and lowest
values in a dataset.
Answer: a) A measure of the average
distance of each value from the mean.

16. Find the mean of the following
dataset: 10, 20, 30, 40, 50
a) 20
b) 30
c) 35
d) 40
Answer: c) 35

17. Find the median of the following
dataset: 2, 4, 6, 8, 10, 12
a) 4
b) 6
c) 8
d) 10
Answer: c) 8

18. What is a random variable?
a) A variable that is not determined by
chance
b) A variable that has a fixed value
c) A variable whose value depends on the
outcome of a random event
d) A variable that can only take on
discrete values
Answer: c) A variable whose value
depends on the outcome of a random
event.

19. What is the expected value of a random
variable?
a) The value that the random variable is most
likely to take on
b) The average value of the random variable
over many trials
c) The highest possible value the random
variable can take on
d) The lowest possible value the random
variable can take on
Answer: b) The average value of the random
variable over many trials.

20. What is the variance of a random variable?
a) A measure of how spread out the values of
the random variable are from the expected
value
b) The highest possible value the random
variable can take on
c) The lowest possible value the random
variable can take on
d) The value that the random variable is most
likely to take on
Answer: a) A measure of how spread out
the values of the random variable are from
the expected value.

21. Which of the following is an
example of a discrete variable?
a) The weight of a person
b) The height of a person
c) The number of cars in a parking
lot
d) The temperature outside
Answer: c) The number of cars
in a parking lot.

22. Which of the following is an example
of a continuous random variable?
a) The number of heads obtained
when flipping a coin
b) The number of students in a
classroom
c) The time it takes to complete a
task
d) The number of cars in a parking lot
Answer: c) The time it takes to
complete a task

23. What is a probability distribution?
a) A set of all possible outcomes of an
experiment
b) A set of probabilities associated with each
outcome of an experiment
c) A set of all possible values of a random
variable
d) A mathematical function that describes the
probabilities of each value of a random variable
Answer: d) A mathematical function that
describes the probabilities of each value of
a random variable

24. Which of the following is the formula
for the mean (expected value) of a
discrete probability distribution?
a) μ = ΣxP(x)
b) μ = ΣP(x)
c) μ = Σx
d) μ = Σ(x - μ)^2P(x)
Answer: a) μ = ΣxP(x)

25. Which of the following is the formula
for the variance of a discrete
probability distribution?
a) σ^2 = ΣxP(x)
b) σ^2 = ΣP(x)
c) σ^2 = Σ(x - μ)^2P(x)
d) σ^2 = Σ(x - μ)
Answer: c) σ^2 = Σ(x - μ)^2P(x)

26. If a coin is tossed, what are the
possible values of the random
variable for the number of heads?
A. 0, 1
B. 0, 1, 2
C. 1, 2, 3
D. 0, 1, 2, 3
A. 0, 1

27. Suppose you tossed two coins. What
are the sample spaces for the
experiment above?
A. HH, TT
B. HH, HT, TT
C. HH, TH, TT
D. HH, HT, TT, TH
D. HH, HT, TT, TH

30. What is the mean of a standard
normal distribution?
a) 0
b) 1
c) -1
d) It depends on the standard
deviation.
Answer: a) 0

31. According to the empirical rule, what
percentage of data is expected to fall
within one standard deviation of the
mean in a normal distribution?
a) 34%
b) 68%
c) 95%
d) 99.7%
Answer: b) 68%

32. According to the empirical rule, what
percentage of data is expected to fall
within two standard deviations of the
mean in a normal distribution?
a) 34%
b) 68%
c) 95%
d) 99.7%
Answer: c) 95%

33. According to the empirical rule, what
percentage of data is expected to fall
within three standard deviations of
the mean in a normal distribution?
a) 34%
b) 68%
c) 95%
d) 99.7%
Answer: d) 99.7%

34. If a normal distribution has a mean of 50 and
a standard deviation of 10, what is the range
of values that contains approximately 95% of
the data, according to the empirical rule?
a) 20 to 80
b) 30 to 70
c) 40 to 60
d) 45 to 55
Answer: b) 30 to 70

35. If a normal distribution has a mean of 100
and a standard deviation of 20, what is the z-
score of a data point that is 120?
a) 1.00
b) 1.50
c) 2.00
d) 2.50
Answer: c) 2.00

36. In a normal distribution, what is the
approximate range of z-scores that contains
99.7% of the data?
a) -3 to 3
b) -2 to 2
c) -1 to 1
d) -4 to 4
Answer: a) -3 to 3

37. If a normal distribution has a mean of 75 and
a standard deviation of 5, what is the
approximate range of values that contains
99.7% of the data, according to the empirical
rule?
a) 60 to 90
b) 65 to 85
c) 70 to 80
d) 73 to 77
Answer: d) 73 to 77

38. A normal distribution has a mean of 100 and
a standard deviation of 10. What is the
approximate range of values that contains
95% of the data, according to the empirical
rule?
a) 80 to 120
b) 85 to 115
c) 90 to 110
d) 93 to 107
Answer: d) 93 to 107

39. A normal distribution has a mean of 50 and a
standard deviation of 5. What percentage of
data falls between the values of 40 and 60?
a) 34%
b) 68%
c) 95%
d) 99.7%
Answer: b) 68%

40. In a normal distribution with a mean of 50
and a standard deviation of 10, what is the
approximate range of values that contains
68% of the data, according to the empirical
rule?
a) 30 to 70
b) 40 to 60
c) 45 to 55
d) 47 to 53
Answer: d) 47 to 53

41. Which of the following is an example
of a random sampling technique?
a) Convenience sampling
b) Stratified sampling
c) Snowball sampling
d) Purposive sampling
Answer: b) Stratified sampling

42. It is a variable being measured to
produce numerical observations
associated with the random outcomes of
a chance experiment.
A. fixed variable
B. dependent variable
C. independent variable
D. random variable
D. random variable

43. A fair coin is tossed three times and the
sequence of heads (H) and tails (T) is
observed. What is the probability that no
heads will appear?
A. 1/8
B. 3/8
C. 5/8
D. 2/3
A. 1/8

44. Evaluate the score of the student in a
biology test where the equivalent z-score
is 0.98. The mean of the test was 88 with
a standard deviation of 9.5.
A. 95
B. 96
C. 97
D. 98
C. 97

47. The record of weights of the male population
follows the normal distribution. Its mean and the
standard deviation are 70 kg and 15 kg respectively.
If a researcher considers the records of 50 males,
what would be its standard deviation?
A. 2.11
B. 2.12
C. 2.13
D. 2.14
B. 2.12

48. What is the estimate, if the sample size of
random sampling using the Central Limit
Theorem is almost normal in accordance with
Statisticians?
A. If n= 2
B. If n= 3
C. If n= 10
D. If n= 30
D. If n= 30

49. Which of the following is not a
probability sampling technique?
A. Simple Random Sampling
B. Systematic Sampling
C. Convenience Sampling
D. Stratified Sampling
Answer: C. Convenience Sampling

50. In stratified sampling, what is the purpose of
dividing the population into strata?
A. To ensure that every member of the population
has an equal chance of being selected
B. To reduce the variability of the sample
C. To increase the representativeness of the sample
D. To reduce the sample size required
Answer: C. To increase the representativeness of
the sample

51. Which of the following is an example of stratified
sampling?
A. Dividing a city into neighborhoods and randomly
selecting households within each neighborhood
B. Selecting every 10th person from a list of employees
C. Randomly selecting customers as they exit a store
D. Dividing a university into departments and randomly
selecting students from each department
Answer: D. Dividing a university into departments and
randomly selecting students from each department

52. What is a null hypothesis?
A. A hypothesis that is always true
B. A hypothesis that is never true
C. A hypothesis that is tested using statistical
methods
D. A hypothesis that is assumed to be true
unless proven otherwise
Answer: D. A hypothesis that is assumed to
be true unless proven otherwise

53. What is a Type I error?
A. Rejecting a true null hypothesis
B. Failing to reject a false null hypothesis
C. Rejecting a false alternative hypothesis
D. Failing to reject a true alternative
hypothesis
Answer: A. Rejecting a true null
hypothesis

54. What is a Type II error?
A. Failing to reject a false null hypothesis
B. Rejecting a true null hypothesis
C. Failing to reject a true alternative
hypothesis
D. Rejecting a false alternative hypothesis
Answer: A. Failing to reject a false null
hypothesis

55. What is the significance level in hypothesis testing?
A. The level of confidence in rejecting the null
hypothesis
B. The level of confidence in failing to reject the
null hypothesis
C. The probability of making a Type I error
D. The probability of making a Type II error
Answer: C. The probability of making a Type I
error

56. Which type of error occurs when a researcher
concludes that there is a significant difference or
relationship between two variables when there is
actually no such difference or relationship?
A. Type I error
B. Type II error
C. Both Type I and Type II errors
D. Neither Type I nor Type II error
Answer: A. Type I error

57. Which type of error occurs when a researcher
concludes that there is no significant difference or
relationship between two variables when there is
actually such a difference or relationship?
A. Type I error
B. Type II error
C. Both Type I and Type II errors
D. Neither Type I nor Type II error
Answer: B. Type II error

58. Which type of error is associated with a
one-tailed hypothesis test?
A. Type I error
B. Type II error
C. Both Type I and Type II errors
D. Neither Type I nor Type II error
Answer: A. Type I error

60. Which of the following describes a
null hypothesis using two-tailed
test?
A. 𝐻0: 𝜇 = 𝜇0
B. 𝐻0: 𝜇 ≠ 𝜇0
C. 𝐻0: 𝜇 ≥ 𝜇0
D. 𝐻0: 𝜇 ≤ 𝜇0

61. Which of the following describes
an alternative hypothesis using
two-tailed test?
A. 𝐻𝑎: 𝜇< 50 𝑦𝑒𝑎𝑟𝑠𝑜𝑙𝑑
𝐵. 𝐻𝑎: 𝜇> 50 𝑦𝑒𝑎𝑟𝑠𝑜𝑙𝑑
C.𝐻𝑎: 𝜇 ≠ 50 𝑦𝑒𝑎𝑟𝑠𝑜𝑙𝑑
D. 𝐻𝑎: 𝜇 = 50 𝑦𝑒𝑎𝑟𝑠𝑜𝑙𝑑

62. Which of the following must be
used as the significance level if we
want a lower possibility of a
correct decision?
A. 1%
B. 2%
C. 5%
D. 10%

63. Which of the following is a Type I
error?
A. 𝐻0 is true; reject 𝐻0.
B. 𝐻0 is false; reject 𝐻0.
C. 𝐻0 is true; fail to reject 𝐻0.
D. 𝐻0 is false; fail to reject 𝐻0.

64. If the computed z-value is 1.286 and the
critical value is 1.383, which of the following
statements could be true?
A. It lies in the rejection region, 𝐻𝑜 must be
rejected.
B. It lies in the rejection region, hence we fail
to reject𝐻𝑜.
C. It lies in the non-rejection region, 𝐻𝑜 must
be rejected.
D. It lies in the non-rejection region, hence
we fail to reject 𝐻𝑜.

65. Using a left-tailed test, which of the
following value of z will not fall in the
rejection region where the critical
value is – 1.638?
A. – 1.637
B. – 1.639
C. – 1.641
D. – 1.706

66. If the computed z-value is 1.915 and the critical
value is 1.812, which of the following statements
could be true?
A. It lies in the rejection region, 𝐻𝑜 must be
rejected.
B. It lies in the rejection region, hence we fail to
reject𝐻𝑜.
C. It lies in the non-rejection region, 𝐻𝑜 must be
rejected.
D. It lies in the non-rejection region, hence we fail
to reject 𝐻𝑜.

67. The numerical measure that describes
the certain characteristics of a
population is called ______________.
A. sample
B. statistics
C. parameter
D. population

68. What is the parameter to be tested in
this claim? As stated by a company’s
shipping department, the number of
shipping errors per million shipments has
a standard deviation of 2.7.
A. million shipments
B. standard deviation of 2.7
C. number of shipping errors
D. company shipping department

69. A vacuum cleaner consumes less than 46
kwh per year. What hypothesis test can
you use in this claim?
A. left-tailed
B. right- tailed
C. null hypothesis
D. alternative hypothesis

70. 41. The sign of the alternative
hypothesis in a left-tailed test is always
________
A. Equal
B. not equal
C. less than
D. greater than

71. A scientist invented a substance that
increases the life of an automobile
battery. If the mean lifetime of the
battery is 24 months, then what are his
hypotheses?
A. 𝐻𝑜: 𝜇 = 24, 𝐻𝑎: 𝜇 ≠ 24
𝐵. 𝐻𝑜: 𝜇 = 24, 𝐻𝑎: 𝜇> 24
C. 𝐻𝑜: 𝜇 = 24, 𝐻𝑎: 𝜇 ≤ 24
D. 𝐻𝑜: 𝑝 = 24, 𝐻𝑎: 𝑝> 24

72. A researcher reports that the average salary of an
accountant is more than ₱40,000. A sample of 30
accountants has a mean salary of ₱42,500. At a = 0.05 test,
it is found that an accountant earns more than ₱40,000 a
month. The standard deviation of the population is
₱3,000. What is the alternative hypothesis?
A. The average salary of an accountant is equal to ₱40,000.
B. The average salary of an accountant is greater than
₱40,000.
C. The average salary of an accountant is less than or equal
to ₱42,500.
D. The average salary of an accountant is greater than or
equal to₱42,500.

73. It was claimed that the average monthly income of
aircraft pilot was ₱116, 714.00. A random sample
of 45 pilots is selected and it is found out that the
average monthly salary is ₱ 120,000. Using a 0.01
level of significance, can it be concluded that there
is an increase in the average monthly income of
pilot?”
A. 𝐻𝑜: µ = ₱116, 714.00, 𝐻𝑎: µ ≤ ₱116, 714.00
B. 𝐻𝑜: µ = ₱116, 714.00, 𝐻𝑎: µ ≠ ₱116, 714.00
C. 𝐻𝑜: µ = ₱116, 714.00, 𝐻𝑎: µ > ₱116, 714.00
D. 𝐻𝑜: µ = ₱116, 714.00, 𝐻𝑎: µ < ₱116, 714.00

74. Which directional test is illustrated in the given
problem below?
In a recent survey, the average amount of money
students have in their wallets is ₱200.00 with a
standard deviation of 45. A teacher feels that the
average amount is lower. She surveyed 80
randomly selected students and found that the
average amount is ₱35.
A. left-tailed
B. two-tailed
C. alternative
D. right-tailed

75. Which of the following is NOT a consideration
in using z-test/statistic?
A. Variance is known.
B. Sample standard deviation is known.
C. The population mean is less than 30.
D. Population standard deviation is known.

76. A leader of an association of jeepney drivers claims
that the average daily take-home pay of all jeepney
drivers in Caloocan is ₱350.00. A random sample of
100 jeepney drivers in Caloocan was interviewed
and the take-home pay was found to be ₱420.00. If
a 0.05 significance level was used to find out
whether the average take-home pay is different
from ₱350.00 and population variance was
assumed to be ₱92.00, what is the appropriate test
statistic?
A. t-test C. left-tailed test
B. z-test D. right-tailed test

77. The value that separates a rejection
region from an acceptance region is
called a ___________.
A. Parameter
B. Hypothesis
C. critical value
D. significance level