Question: Sample study of two sleeping pills, a new one and an older pill. two thousand randomly divided groups are divided in to two groups. First group gets old pill, and second group gets new pill. the time required to fall asleep after pill is administered is recorded. for each person. The results are as followed

x 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


group 1 group 2
n 1000 n 1000
x 15.4 min x 15.0 min
s 3.5 min s 3.0 min

Consider the test of hypothesis H0 m 1- m 2=0 versus H1: m 1- m2 >0 where M1 and M2 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 .025 significance level.
c. Find the 95% confidence interval for m1-m2.
d. for what values of the difference between the two sample means would one have to reject the null hypothesis? Here you will need to solve and inequality. Note that the test statistic would need to exceed the prescribed critical value.