Reference no: EM132488209

Problem: Data was collected on annual personal time (in hours) taken by a random selection of 50 women and 55 men employed by a medium-sized company. We know that the data for women and men is normally distributed. The Human Resources Department believes that the amount of personal time used by women is less than the amount of personal time used by men.

The sample of women took an average of 25 hours of personal time with a standard deviation of 4.9 hours. The men took an average of 27.6 hours of personal time with a standard deviation of 4.8 hours. Assuming the population standard deviations are equal, test the Human Resources Departments claim at α = 0.05.

A. Write out the hypotheses for this test.

H₀:

H_A:

B. Find the test statistic and p-value for this test. Show which calculator function you are using.

C. Using either the p-value or the test statistic what is our decision about the H₀.

D. What conclusion did you come to in context to this test?

E. Calculate the 90% confidence interval for the difference between the average number of hours of personal time used by women and men. Show which calculator function you are using.