10.128 [EX10-128] Americans snooze on the weekends, according to a poll of 1506 adults for the National Sleep Foundation and reported in a USA Snapshot during April 2005.

Hours of Sleep Weekdays Weekends Less than 6 0.16 0.10 6–6.9 0.24 0.15 7–7.9 0.31 0.24 8 or more 0.26 0.49 Two independent random samples were taken at a large industrial complex. The workers selected in one sample were asked, “How many hours, to the nearest 15 minutes, did you sleep on Tuesday night this week?” The workers selected for the second sample were asked, “How many hours, to nearest 15 minutes, did you sleep on Saturday night last weekend?”

Weekday Weekend 5.00 7.75 7.25 9.00 7.25 8.75 7.50 9.25 7.25 8.75 6.25 5.25 9.25 9.25 7.00 7.75 6.75 7.50 8.50 8.75 6.50 9.25 7.00 7.75 8.00 8.75 9.50 8.00 9.25 9.25 6.00 8.75 7.75 8.75 7.50

a. Construct a histogram and find the mean and standard deviation for each set of data.

b. Do the distributions of “hours of sleep on weekday” and “hours of sleep on weekend” resulting from the poll appear to be similar in shape? center? spread? Discuss your responses.

c. Is it possible that both of the samples were drawn from normal populations? Justify your answer.

d. Is the mean number of hours slept on the weekend statistically greater than the mean number of hours slept on the weekday? Use

  0.05.

e. Is there sufficient evidence to show that the standard deviation of these two samples are statistically different? Use   0.05.

f. Explain how the answers to parts b–e now affect your thoughts about your answer to part a.