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Slide 1
Hypothesis Testing
Slide 2
What is a Hypothesis? n Claim Average Weekly Entertainment
Spending is 55? n How would you test that claim?
Slide 3
How to Test a Hypothesis
Slide 4
Hypothesis Testing n Statistical hypothesis testing represents
a formal, systematic approach to evaluating data, and deciding
whether the results from an observed sample of data can be
generalized to a larger population, or if instead the results might
just be due to chance.
Slide 5
Who Likes Wallace and Gromit? n Potential Hypothesis about the
Wallace and Gromit (W&G): Males prefer W&G to Females
Slide 6
Who Likes Wallace and Gromit? n Potential Hypothesis about the
Wallace and Gromit (W&G): Males prefer W&G to Females
Greeks prefer the W&G over independents
Slide 7
Who Likes Wallace and Gromit? n Potential Hypothesis about the
Wallace and Gromit (W&G): Males prefer W&G to Females
Greeks prefer the W&G over independents If you have heard about
W&G you will prefer them over people who have not heard of the
W&G
Slide 8
Who Likes Wallace and Gromit? n Potential Hypothesis about the
Wallace and Gromit (W&G): Males prefer W&G to Females
Greeks prefer the W&G over independents If you have heard about
W&G you will prefer them over people who have not heard of the
W&G If you have watched the W&G you will prefer them over
people who have not watched the W&G
Slide 9
Who Likes Wallace and Gromit? n Potential Hypothesis about the
Wallace and Gromit (W&G): Males prefer W&G to Females
Greeks prefer the W&G over independents If you have heard about
W&G you will prefer them over people who have not heard of the
W&G If you have watched the W&G you will prefer them over
people who have not watched the W&G If you have lived outside
the USA for more than 6 months you will prefer W&G over people
who have lived in the USA
Slide 10
Who Likes Wallace and Gromit? n Potential Hypothesis about the
Wallace and Gromit (W&G): Males prefer W&G to Females
Greeks prefer the W&G over independents If you have heard about
W&G you will prefer them over people who have not heard of the
W&G If you have watched the W&G you will prefer them over
people who have not watched the W&G If you have lived outside
the USA for more than 6 months you will prefer W&G over people
who have lived in the USA A greater percentage of people who have
lived outside of the USA have watched W&G previously
Slide 11
Checking out Wallace and Gromit
Slide 12
Wallace and Gromit Questionnaire n Survey is Anonymous
Slide 13
Wallace and Gromit Questionnaire n Survey is Anonymous n Age n
Gender n Member of a fraternity or sorority n Ever lived out side
of the USA for more than 6 months
Slide 14
Wallace and Gromit Questionnaire n Survey is Anonymous n Age n
Gender n Member of a fraternity or sorority n Ever lived out side
of the USA for more than 6 months n Ever heard of Wallace and
Gromit n Ever watched Wallace and Gromit If so, when was last time
watched
Slide 15
Wallace and Gromit Questionnaire n Survey is Anonymous n Age n
Gender n Ever lived out side of the USA for more than 6 months n
Member of a fraternity or sorority n Ever heard of Wallace and
Gromit n Ever watched Wallace and Gromit If so, when was last time
watched n Rate on scale from 1 to 5 (1 = strongly disagree; 5 =
strongly agree) Wallace and Gromit is clever comedy Wallace and
Gromit is my kind of entertainment Would watch Wallace and Gromit
again at home
n Example 1: Over a period of years, a toothpaste has received
a mean customer satisfaction rating of 5.9 out of 7. Because of a
change in suppliers, there is concern that customer satisfaction
may have decreased. In a sample of 60 customers, the mean rating is
found to be 5.60, with a standard deviation of 0.87.
Slide 18
Hypothesized Mean Hypothesized Mean
Slide 19
Toothpaste Example 1.Business question: 2.Null hypothesis (H 0
): 3.Alternative hypothesis (H a ): 4.Test statistic: 5.Rejection
region:
Slide 20
Toothpaste Example 1.Business question: Has Customer
Satisfaction Decreased? 2.Null hypothesis (H 0 ): 3.Alternative
hypothesis (H a ): 4.Test statistic: 5.Rejection region:
Slide 21
Toothpaste Example 1.Business question: Has Customer
Satisfaction Decreased? 2.Null hypothesis (H 0 ): Try to Prove
Wrong! 3.Alternative hypothesis (H a ): 4.Test statistic:
5.Rejection region:
Slide 22
Toothpaste Example 1.Business question: Has Customer
Satisfaction Changed? 2.Null hypothesis (H 0 ): Try to Prove Wrong!
= True Mean equals the Hypothesized Mean 3.Alternative hypothesis
(H a ): 4.Test statistic: 5.Rejection region:
Slide 23
Toothpaste Example 1.Business question: Has Customer
Satisfaction Changed? 2.Null hypothesis (H 0 ): Try to Prove Wrong!
= True Mean equals the Hypothesized Mean = True Average Equals
3.Alternative hypothesis (H a ): 4.Test statistic: 5.Rejection
region:
Slide 24
Toothpaste Example 1.Business question: Has Customer
Satisfaction Changed? 2.Null hypothesis (H 0 ): Try to Prove Wrong!
= True Mean equals the Hypothesized Mean = True Average Equals
3.Alternative hypothesis (H a ): What We Really Think! 4.Test
statistic: 5.Rejection region:
Slide 25
Toothpaste Example 1.Business question: Has Customer
Satisfaction Changed? 2.Null hypothesis (H 0 ): Try to Prove Wrong!
= True Mean equals the Hypothesized Mean = True Average Equals
3.Alternative hypothesis (H a ): What We Really Think! Something
Has Changed 4.Test statistic: 5.Rejection region:
Slide 26
Toothpaste Example 1.Business question: Has Customer
Satisfaction Changed? 2.Null hypothesis (H 0 ): Try to Prove Wrong!
= True Mean equals the Hypothesized Mean = True Average Equals
3.Alternative hypothesis (H a ): What We Really Think! Something
Has Changed True Average Not Equal to 4.Test statistic: 5.Rejection
region:
Slide 27
Toothpaste Example 1.Business question: Has Customer
Satisfaction Changed? 2.Null hypothesis (H 0 ): Try to Prove Wrong!
= True Mean equals the Hypothesized Mean = True Average Equals
3.Alternative hypothesis (H a ): What We Really Think! Something
Has Changed True Average Not Equal to 4.Test statistic:Test using a
Z-score 5.Rejection region:
Slide 28
Toothpaste Example 1.Business question: Has Customer
Satisfaction Changed? 2.Null hypothesis (H 0 ): Try to Prove Wrong!
= True Mean equals the Hypothesized Mean = True Average Equals
3.Alternative hypothesis (H a ): What We Really Think! Something
Has Changed True Average Not Equal to 4.Test statistic:Test using a
Z-score 5.Rejection region: If Z-score,
Slide 29
Toothpaste Example 1.Business question: Has Customer
Satisfaction Changed? 2.Null hypothesis (H 0 ): Try to Prove Wrong!
= True Mean equals the Hypothesized Mean = True Average Equals
3.Alternative hypothesis (H a ): What We Really Think! Something
Has Changed True Average Not Equal to 4.Test statistic:Test using a
Z-score 5.Rejection region: If Z-score, based on ,
Slide 30
Toothpaste Example 1.Business question: Has Customer
Satisfaction Changed? 2.Null hypothesis (H 0 ): Try to Prove Wrong!
= True Mean equals the Hypothesized Mean = True Average Equals
3.Alternative hypothesis (H a ): What We Really Think! Something
Has Changed True Average Not Equal to 4.Test statistic:Test using a
Z-score 5.Rejection region: If Z-score, based on , is unusual --
far away from 0, reject Null Hypothesis
Slide 31
Toothpaste Example n Example 1: Over a period of years, a
toothpaste has received a mean customer satisfaction rating of 5.90
out of 7. Because of a change in suppliers, there is concern that
customer satisfaction may have decreased. In a sample of 60
customers, the mean rating is found to be 5.60, with a standard
deviation of 0.87. n The Z-score:
Slide 32
Hypothesized Mean How Unusual is Z = -2.67?
Slide 33
Slide 34
Toothpaste Example 5.Rejection region: Depends on Confidence
Level 6.Observed test statistic: 7.p-value: 8.Statistical
conclusion: 9.Business conclusion:
Slide 35
Toothpaste Example 5.Rejection region: Depends on Confidence
Level 95% Confidence Level, if Z > 1.96 or Z < -1.96, Reject
Null 6.Observed test statistic: 7.p-value: 8.Statistical
conclusion: 9.Business conclusion:
Slide 36
Reject Accept 95% Rejection Region
Slide 37
Reject 90% Region Other Rejection Regions -1.6451.645 -2.572.57
99% RegionReject
Slide 38
Toothpaste Example 5.Rejection region: Depends on Confidence
Level 95% Confidence Level, if Z > 1.96 or Z < -1.96, Reject
Null 6.Observed test statistic: Already Calculated z = -2.67
7.p-value: 8.Statistical conclusion: 9.Business conclusion:
Slide 39
Toothpaste Example 5.Rejection region: Depends on Confidence
Level 95% Confidence Level, if Z > 1.96 or Z < -1.96, Reject
Null 6.Observed test statistic: Already Calculated z = -2.67
7.p-value: 8.Statistical conclusion: Reject Null Hypothesis
9.Business conclusion:
Slide 40
Toothpaste Example 5.Rejection region: Depends on Confidence
Level 95% Confidence Level, if Z > 1.96 or Z < -1.96, Reject
Null 6.Observed test statistic: Already Calculated z = -2.67
7.p-value: 8.Statistical conclusion: Reject Null Hypothesis
9.Business conclusion: Average Customer Satisfaction Has Changed In
Particular, Decreased.
Slide 41
Toothpaste Example 5.Rejection region: Depends on Confidence
Level 95% Confidence Level, if Z > 1.96 or Z < -1.96, Reject
Null 6.Observed test statistic: Already Calculated z = -2.67
7.p-value: pr(z 2.67) 8.Statistical conclusion: Reject Null
Hypothesis 9.Business conclusion: Average Customer Satisfaction Has
Changed In Particular, Decreased
Slide 42
p-value n The p-value is a measure of the evidence against H 0
; it is the probability of observing the test statistic z given
that H 0 is true.
Slide 43
p-value n The p-value is a measure of the evidence against H 0
; it is the probability of observing the test statistic z given
that H 0 is true. Small p-value (accept/reject) H 0 Large p-value
(accept/reject) H 0
Slide 44
pr(z 2.67) p-value 2 x pr(z>2.67) = 2 x (0.0038) p-value =
(0.0076)