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Hypothesis Testing

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What is a Hypothesis? n Claim Average Weekly Entertainment Spending is 55? n How would you test that claim?

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How to Test a Hypothesis

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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.

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Who Likes Wallace and Gromit? n Potential Hypothesis about the Wallace and Gromit (W&G): Males prefer W&G to Females

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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

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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

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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

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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

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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

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Checking out Wallace and Gromit

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Wallace and Gromit Questionnaire n Survey is Anonymous

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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

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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

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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

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Hypothesis Testing Structure 1.Business question: 2.Null hypothesis (H 0 ): 3.Alternative hypothesis (H a ): 4.Test statistic: 5.Rejection region: 6.Observed test statistic: 7.p-value: 8.Statistical conclusion: 9.Business conclusion:

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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.

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Hypothesized Mean Hypothesized Mean

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Toothpaste Example 1.Business question: 2.Null hypothesis (H 0 ): 3.Alternative hypothesis (H a ): 4.Test statistic: 5.Rejection region:

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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:

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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:

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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:

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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:

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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:

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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:

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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:

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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:

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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,

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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 ,

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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

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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:

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Hypothesized Mean How Unusual is Z = -2.67?

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Toothpaste Example 5.Rejection region: Depends on Confidence Level 6.Observed test statistic: 7.p-value: 8.Statistical conclusion: 9.Business conclusion:

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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:

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Reject Accept 95% Rejection Region

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Reject 90% Region Other Rejection Regions -1.6451.645 -2.572.57 99% RegionReject

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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:

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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:

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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.

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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

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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.

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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

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pr(z 2.67) p-value 2 x pr(z>2.67) = 2 x (0.0038) p-value = (0.0076)