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Stats 309 PPT hypothesis testing ex

# Stats 309 PPT hypothesis testing ex - Examples The...

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Examples The Vividness of Visual Imagery Questionnaire (VVIQ) is widely used by behaviorists to assess visual imagery. Researchers administered the VVIQ to a sample of 51 college students on varsity sports teams. The mean of the VVIQ scores was 65.60 and the population standard deviation was 19.38. In the general population, the mean VVIQ score is 67. Conduct a test to determine whether the mean VVIQ score of college athletes is less than 67. Use α = .01. 52 . 51 38 . 19 67 60 . 65 ) 2 * - = - = Z 1)H 0 :µ = 67 H a :µ < 67 65.60 19.38 51 x n σ = = = 33 . 2 Z if H Reject 33 . 2 01 . ) 3 * 0 01 . - < = = Z α 4)Conclusion: Since Z * =-.52 is not < -2.33, we have insufficient evidence to reject H 0 at the .01 significance level.

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A researcher wanted to study the relationship of employment status to mental health. Each of a sample of 49 unemployed men was given a mental health examination with lower scores indicating better mental health. The mean of the sample was 10.94 and the population standard deviation is 5.10. Test to see if the mean score for all unemployed men exceeds 9. Use α = .05. 66 . 2 49 10 . 5 9 94 . 10 ) 2 * = - = Z 1)H 0 :µ = 9 H a :µ > 9 10.94 5.10 49 x n σ = = = . 645 . 1 Z if H Reject 645 . 1 Z 05 . ) 3 * 0 .05 = = α 4) Conclusion: Since Z * = 2.66 is > 1.645, we have sufficient evidence to reject H 0 and accept H a that the mean score for all unemployed men exceeds 9 at the .05 significance level.
P-values The Rejection Region method produces a ‘yes or no’ response to the question ‘Is there sufficient evidence to infer that the alternative hypothesis is true?’.

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