1 Following is the data I collected from your class and the

1. Following is the data I collected from your class and the class I taught this spring for the number of hours of sleep you reported receiving the night before the first class. Summer 3.0 4.0 6.0 6.0 6.0 6.0 6.5 7.0 7.0 7.0 7.0 7.5 8.0 8.0 8.0 8.0 8.5-9 Spring 4.0 4.5 5.0 6.0 6.0 6.0 6.0 6.0 6.5 7.0 7.0 7.0 7.5 7.5 7.5 7.5 8.0 8.0 8.0 8.0 8.5 a. For each group. calculate the mean, standard deviation and 95% confidence intervals for the hours of sleep students receive. b. Use the confidence intervals to make a statement about the average amount of sleep students in the population get and explain what this tells us. Compare the intervals for each class and comment on whether the intervals appear to come from different populations. c. Based on your analysis. do students in either the summer or the spring appear to get the required 8 hours of sleep on average? Use the confidence intervals to explain your reasoning.

Solution

The number of sleep hours is assumed to follow a normal distribution.

(a) The mean and standard deviation for the summer sleep hours respectively are 6.7353 and 1.5321. Also, the 95% CI for the summer sleep hours is (5.9475, 7.5230).

The mean and standard deviation for the spring sleep hours respectively are 6.7381 and 1.2310. The 95% CI for the spring sleep hours is (6.1777,7.2985).

(b) The mean of either of the sleep hours, summer or spring, lie in the 95% CI of other parameter. Thus, the means are not significantly different from each other.

(c) The 8 hours of sleep does not lie in the 95% CI of either summer sleep hours or the spring sleep hours. Hence, it can be said that the students do not get the required 8 hours of sleep either in summer of the spring.