# Question

A new type of sleeping pill is tested against an older, standard pill. Two thousand insomniacs are randomly divided into two equal groups. The first group is given the old pill, and the second group receives the new pill. The time required to fall asleep after the pill is administered is recorded for each person. The results of the experiment are given in the following table, where and s represent the mean and standard deviation, respectively, for the times required to fall asleep for people in each group after the pill is taken.

Consider the test of hypothesis H0: µ1 – µ2 = 0 versus H1: µ1 – µ2 > 0, where µ1 and µ2 are the mean times required for all potential users to fall asleep using the old pill and the new pill, respectively.

a. Find the p-value for this test.

b. Does your answer to part a indicate that the result is statistically significant? Use α = .025.

c. Find a 95% confidence interval for µ1 – µ2.

d. Does your answer to part c imply that this result is of great practical significance?

Consider the test of hypothesis H0: µ1 – µ2 = 0 versus H1: µ1 – µ2 > 0, where µ1 and µ2 are the mean times required for all potential users to fall asleep using the old pill and the new pill, respectively.

a. Find the p-value for this test.

b. Does your answer to part a indicate that the result is statistically significant? Use α = .025.

c. Find a 95% confidence interval for µ1 – µ2.

d. Does your answer to part c imply that this result is of great practical significance?

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