Do people who work long hours have more trouble sleeping? This question was examined in the paper “Long Working Hours and Sleep Disturbances: The Whitehall II Prospective Cohort Study” (Sleep [2009]: 737–745). The data in the accompanying table are from two independently selected samples of British civil service workers. The authors of the paper believed that these samples were representative of full-time British civil service workers who work 35 to 40 hours per week and of British civil service workers who work more than 40 hours per week.

The question of interest is whether the proportion of workers who usually get less than 7 hours of sleep a night is greater for those who work more than 40 hours per week than for those who work between 35 and 40 hours per week.

a. What hypotheses should be tested to answer the question of interest?

b. Are the two samples large enough for the large-sample test for a difference in population proportions to be appropriate?

c. Based on the following Minitab output, what is the value of the test statistic and what is the value of the associated P-value? If a significance level of 0.01 is selected for the test, will you reject or fail to reject the null hypothesis?

Test and CI for Two Proportions

Difference = p (1) – p (2)

Estimate for difference: 0.0748235

95% lower bound for difference: 0.0410491

Test for difference = 0 (vs > 0): Z = 3.63

P-Value = 0.000

d. Interpret the result of the hypothesis test in the context of this problem.

Number who usually get less than 7 hours Work over 40 hours per week Work 35-40 hours per week n of sleep a night 1,501 958 407 Sample XN ample p 750 1501 0499667 407 958 0424843