3. A health psychologist knew that corporate executives in general have an avera

Question

3. 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

Below are the null and alternate hypothesis
H0: mu equals to 80
H1: mu not equals to 80

Here we use t-test
test statistics, t = (xbar - mu)/(sigma/sqrt(n))
t = (72 - 80) / (13.28/sqrt(20) = -2.6941

Here degrees of freedom = 20 - 1 = 19
p-value = 0.0144

Significance level = 0.05
As p-value is less than significance level, we reject the null hypothesis.
This means there is significant difference between the stress.

This test is most appropriate for this data because of below resons
1. Population variance is unknown
2. Sample size < 30

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