A health psychologist knew that corporate executives in general have an average

Question

A health psychologist knew that corporate executives in general have an average score of 80 on a stress inventory. Population variance is unknown. In order to learn whether corporate executives who exercise regularly have lower stress scores, the psychologist measured the stress of 20 exercising executives and found them to have a mean score of 72. Is this difference significant at the .05 level?

A) What are the null and research hypotheses?

B) Conduct the appropriate hypothesis test by hand. Follow the five steps of hypothesis testing and provide a drawing.

C) Give an interpretation of this data (one sentence conclusion of the hypothesis test that should be free of statistical jargon) and report the statistics in APA format.

D) Explain why the test you chose is the most appropriate.

SD = 13.28

SS = 41.22

Explanation / Answer

(A) Ho: 80 versus Ha: < 80

(B)

Data:    

n = 20   

= 80   

s = 13.28   

x-bar = 72   

Hypotheses:    

Ho: ³ 80   

Ha: < 80   

Decision Rule:    

= 0.05   

Degrees of freedom = 20 - 1 = 19

Critical t- score = -1.729132792   

Reject Ho if t < -1.729132792   

Test Statistic:    

SE = s/n = 13.28/20 = 2.969498274

t = (x-bar - )/SE = (72 - 80)/2.96949827411972 = -2.694057804

p- value = 0.007186142   

Decision (in terms of the hypotheses):    

Since -2.694057804 < -1.729132792 we reject Ho and accept Ha

(C) Conclusion (in terms of the problem):   

It appears that the stress level < 80

(D) We chose the t- test for a single sample because the population variance is unknown and the sample size < 30.

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