INTRODUCTION
CHARACTERISTICS OF A HYPOTHESIS
CRITERIA FOR HYPOTHESIS CONSTRUCTION
STEPS IN HYPOTHESIS TESTING
SOURCES OF HYPOTHESIS
APPROACHES TO HYPOTHESIS TESTING
THE LOGIC OF HYPOTHESIS TESTING
TYPES OF ERRORS IN HYPOTHESIS
Get ready to face Data Science interviews with this set of Statistics questions. This will help you have insight upon the important statistics concepts that are frequently asked in interviews.
INTRODUCTION
CHARACTERISTICS OF A HYPOTHESIS
CRITERIA FOR HYPOTHESIS CONSTRUCTION
STEPS IN HYPOTHESIS TESTING
SOURCES OF HYPOTHESIS
APPROACHES TO HYPOTHESIS TESTING
THE LOGIC OF HYPOTHESIS TESTING
TYPES OF ERRORS IN HYPOTHESIS
Get ready to face Data Science interviews with this set of Statistics questions. This will help you have insight upon the important statistics concepts that are frequently asked in interviews.
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Detailed discussion about the types of statistics form Measures of Central Tendency, Measures of Dispersion, Skewness, Kurtosis, Probability Distributions and much more with their uses cases
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TSTD 6251 Fall 2014SPSS Exercise and Assignment 120 PointsI.docxnanamonkton
TSTD 6251 Fall 2014
SPSS Exercise and Assignment 1
20 Points
In this class, we are going to study descriptive summary statistics and learn how to construct box plot. We are still working with univariate variable for this exercise.
Practice Example:
Admission receipts (in million of dollars) for a recent season are given below for the
n =
30 major league baseball teams:
19.4 26.6 22.9 44.5 24.4 19.0 27.5 19.9 22.8 19.0 16.9 15.2 25.7 19.0 15.5 17.1 15.6 10.6 16.2 15.6 15.4 18.2 15.5 14.2 9.5 9.9
10.7 11.9 26.7 17.5
Require:
a. Compute the mean, variance and standard deviation.
b. Find the sample median, first quartile, and third quartile.
c. Construct a boxplot and interpret the distribution of the data.
d. Discuss the distribution of this set of data by examining kurtosis and skewness
statistics, such as if the distribution is skewed to one side of the distribution, and if the
distribution shows a peaked/skinny curve or a spread out/flat curve.
SPSS Procedures for Computing Summary Statistics
:
Enter the 30 data values in the first column of SPSS
Data View
Tab
Variable View
and name this variable
receipts
Adjust
Decimals
to 3 decimal points
Type
Admission Receipts
($ mn)
in the
Label
column for output viewer
Return to
Data View
and click
A
nalyze
on the menu bar
Click the second menu
D
e
scriptive Statistics
Click
F
requencies …
Move
Admission Receipts
to the
Variable(s)
list by clicking the arrow button
Click
S
tatistics …
button at the top of the dialog box
Now, you can select the descriptive statistics according to what the question requires. For this practice question, it requires central tendency, dispersion, percentile and distribution statistics, so we click all the boxes
except for
P
ercentile(s): and Va
l
ues are group midpoints
.
Click
Continue
to return to the
Frequencies
dialog box
Click
OK
to generate descriptive statistic output which is pasted below:
The first table provides summary statistics and the second table lists frequencies, relative frequencies and cumulative frequencies. The statistics required for solving this problem are highlighted in red.
Statistics
Admission Receipts
N
Valid
30
Missing
0
Mean
18.76333
Std. Error of Mean
1.278590
Median
17.30000
Mode
19.000
Std. Deviation
7.003127
Variance
49.043782
Skewness
1.734
Std. Error of Skewness
.427
Kurtosis
5.160
Std. Error of Kurtosis
.833
Range
35.000
Minimum
9.500
Maximum
44.500
Sum
562.900
Percentiles
10
10.61000
20
14.40000
25
15.35000
30
15.50000
40
15.84000
50
17.30000
60
19.00000
70
19.75000
75
22.82500
80
24.10000
90
26.69000
Admission Receipts
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
9.500
1
3.3
3.3
3.3
9.900
1
3.3
3.3
6.7
10.600
1
3.3
3.3
10.0
10.700
1
3.3
3.3
13.3
11.900
1
3.3
3.3
16.7
14.200
1
3.3
3.3
20.0
15.2.
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3. Probability is a measure of how likely it is for an event to
happen.
We name a probability with a number from 0 to 1.
If an event is certain to happen, then the probability of the
event is 1 and certain not to happen, then the probability of
the event is 0.
Coin Flip with a Fair Coin
P(H) = .5
P(T) = .5
Basic Probability
4. If it is uncertain whether or not an event will happen, then
its probability is some fraction between 0 and 1 (or a
fraction converted to a decimal number).
0 1
Certain not
to happen
Equally likely to
happen or not to happen Certain to
happen
0%
50 %
Chance
100%
12. When two events are statistically independent, it means
that knowing whether one of them occurs makes it
neither more probable nor less probable that the other
occurs.
the occurrence of one event occurs does not affect the
outcome of the occurrence of the other event. Similarly,
when we assert that two random variables are
independent, we intuitively mean that knowing
something about the value of one of them does not
yield any information about the value of the other.
Statistical Independence
13. Example: The number appearing on the upward face of
a die the first time it is thrown and that appearing on the
same die the second time, are independent. e.g. the
event of getting a "1" when a die is thrown and the
event of getting a "1" the second time it is thrown are
independent.
Statistical Independence
14. Basic Probability:
Coins
What is the Prob of Heads v. Tails?
What is the Prob of TT?
What is the Prob of HHH,?
What is the Prob of HTT?
19. Basic
Probability
A Deck of Cards
1. A red card
2. A spade
3. Not a spade
4. An ace
5. Not an ace
6. The ace of spades
7. A picture card
8. A number card or ‘not a picture card‘
9. A card that is either a heart or a club
10. A 4 or 5 but not a spade
11. An even numbered card
20. 1. A red card 26/52 ½
2. A spade 13/52 ¼
3. Not a spade 39/52 ¾
4. An ace 4/52 1/13
5. Not an ace 48/52 12/13
6. The ace of spades 1/52
7. A picture card 12/52 3/13
8. A number card or ‘not a picture card’ 40/52 10/13
9. A card that is either a heart or a club 26/52 ½
10. A 4 or 5 but not a spade 6/52 3/26
11. An even numbered card 20/52 5/13
23. Let's say that our universe contains the numbers
1, 2, 3, and 4.
Let A be the set containing the numbers 1 and 2; that is,
A = {1, 2}.
(Warning: The curly braces are the customary notation for
sets. Do not use parentheses or square brackets.)
Let B be the set containing the numbers
2 and 3; that is, B = {2, 3}. Then we
have the following relationships, with
pinkish shading marking the solution
"regions" in the Venn diagrams:
24. Let's say that our
universe contains the
numbers 1, 2, 3, and
4.
Let A be the set
c o n t a i n i n g t h e
numbers 1 and 2;
that is, A = {1, 2}.
Let B be the set
c o n t a i n i n g t h e
numbers 2 and 3;
that is, B = {2, 3}.
29. Probability: mathematical theory that describes
uncertainty
Statistics: series of techniques for describing and
extracting useful information from data
Probability Versus Statistics
30. The arithmetic mean (or average) is
the sum of a series dividing by how
many numbers you added together.
31. Sum of Series of Numbers
Total # of Numbers in the Series
_____________________________________________________________________________
Mean =
32. Lets Talk About Notation ...
x1, x2, x3 x4 .... xn
5, 7, 11, 13 ....
x bar
the Nth Term
Called
33. Lets Talk About Notation ...
x1, x2, x3 x4 .... xn
5, 7, 11, 13 ....
x bar
the Nth Term
Called
34. Calculating Measures of
Central Tendency
Series 1: 0, 0, 0, 0, 50, 50, 100, 100, 100, 100
Series 2: 10, 20, 30, 40, 50, 50, 60, 70, 80, 90, 100
Series 3: 55, 60, 75, 77, 80, 83, 83, 83, 88, 91, 93
Please Calculate the arithmetic mean
35. Measures of Central Tendency
The number that occurs most frequently is
the mode.
When numbers are arranged in numerical
order, the middle one is the median.
36. Measures of Central Tendency
Series 1: 0, 0, 0, 0, 50, 50, 100, 100, 100, 100
Series 2: 10, 20, 30, 40, 50, 50, 60, 70, 80, 90, 100
Series 3: 55, 60, 75, 77, 80, 83, 83, 83, 88, 91, 93
Please Calculate the Median & Mode
39. Range
Range is the difference between the largest
and smallest values in a set of values.
For example, consider the following numbers:
1, 2, 4, 7, 8, 9, 11.
For this set of numbers, the range would be
11 - 1 or 10.
40. Range &
Interquartile Range
The interquartile range (IQR) is a measure of
variability, based on dividing a data set into
quartiles
The interquartile range is equal to Q3 minus Q1
41. Range &
Interquartile Range
The interquartile range (IQR) is a measure of
variability, based on dividing a data set into
quartiles
The interquartile range is equal to Q3 minus Q1
Example:
0, 10, 20, 30, 40, 50, 50, 60, 70, 80, 90, 100