Investigation 10: Sleepless drivers (due Wed, Feb 15)

You may work with one other person on this assignment, handing in one report with both names.  Word-processed reports are preferred to hand-written ones. Please copy/paste relevant, well-labeled Minitab output into a Word file as appropriate.

In the New Zealand study about car crashes and sleep habits, researchers also asked about how much sleep the subjects had gotten in the previous night. Of those who responded, 65 in the crash group said that they got five hours or less, compared to 464 who got more than five hours. In the control group, 30 said that they got five hours or less, compared to 554 who got more than five hours.

a) Calculate the sample proportion in each group who got five hours or less of sleep in the previous night.

b) Conduct a chi-square test of whether these data provide strong evidence that those in the crash group are more likely to have gotten five hours or less sleep on the previous night. Report the hypotheses, show the calculation of the test statistic, and report the P-value. Also summarize your conclusion.

c) Calculate the relative risk and the odds ratio of getting five hours or less of sleep in the crash group compared to the control group.

d) Determine a 95% confidence interval and a 99% confidence interval for the population odds ratio.

e) Comment on the importance of whether these intervals includes the value 1.

f) Is this an observational study or an experiment? Explain how you can tell. Also describe the implications of this for drawing cause-and-effect conclusions between sleep and car crashes.