The Baltimore Sun (Haney, 21 February 1995) reported on a study by Dr. Sara Harkness in which she compared the sleep patterns of 6-month-old infants in the United States and the Netherlands. She found that the 36 U.S. infants slept an average of just under 13 hours out of every 24, whereas the 66 Dutch infants slept an average of almost 15 hours.
a. The article did not report a standard deviation, but suppose it was 0.5 hour for each group. Compute the standard error of the mean (SEM) for the U.S. babies.
b. Continuing to assume that the standard deviation is 0.5 hour, compute an approximate 95% confidence interval for the mean sleep time for 6-month-old babies in the United States.
c. Continuing to assume that the standard deviation for each group is 0.5 hour, compute an approximate 95% confidence interval for the difference in average sleep time for 6-month-old Dutch and U. S. infants.