Chapter 11.5, Problem 25E

Do the data in Exercise 11.19 present sufficient evidence to indicate that the number of errors is linearly related to the number of hours without sleep?

1. a Give bounds on the attained significance level.
2. b Applet Exercise Determine the exact p-value.
3. c Based on your answers to parts (a) and/or (b), what would you conclude at the α = .05 level of significance?
4. d Would you expect the relationship between y and x to be linear if x were varied over a wider range, say, from x = 4 to x = 48?
5. e Give a 95% confidence interval for the slope. Provide a practical interpretation for this interval estimate.

11.19 A study was conducted to determine the effects of sleep deprivation on subjects’ ability to solve simple problems. The amount of sleep deprivation varied over 8, 12, 16, 20, and 24 hours without sleep. A total of ten subjects participated in the study, two at each sleep-deprivation level. After his or her specified sleep-deprivation period, each subject was administered a set of simple addition problems, and the number of errors was recorded. The results shown in the following table were obtained.

1. a Find the least-squares line appropriate to these data.
2. b Plot the points and graph the least-squares line as a check on your calculations.
3. c Calculate S².