Question

A health psychologist knew that corporate executives in general have an average score of 80 with a standard deviation of 12 on a stress inventory and that the scores are normally distributed. 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 significant at the .05 level? SD=13.28, SS=41.22

A) What is the appropriate test for this data?

B) Conduct the appropriate hypothesis test.
1. Research hypothesis and null hypothesis.

2. Population mean:
Population variance:
Variance of the distribution of means
Standard deviation of the distribution of sample means:
Shape of the comparison distribution:
Z=(M-μ_M)/σ_M
3. Is this a .05 significance cutoff?
4. Do we reject or fail to reject the null hypothesis

Answer 1

A) One sample z-test for population mean.

B)

1)

2) Population mean = 80

Population variance = (12)^2 = 144

  

The test statistic is

  

P-value = P(Z < -2.98)

= 0.0014

Since the p-value is less than the significance

level, so should reject the null hypothesis.