# Paired Difference Test

A paired difference experiment produced the following results

a) Determine the values of z for which the null hypothesis, m1 -m2 = 0, would be rejected in favor of the alternative hypothesis, m1 - m2 < 0. Use a = 0.10

b) Conduct the paired difference test described in part a. Draw the appropriate conclusions.

c) What assumptions are necessary so that the paired difference test will be valid.

d) Find a 90% confidence interval for the mean difference.

https://brainmass.com/statistics/normal-distribution/paired-difference-test-271900

#### Solution Preview

Here it is given that,

= 38, = 92, = 95.5, = -3.5, = 21

Since the sample size >30, the test statistic for testing the null hypothesis is given by,

follows a Standard Normal distribution.

a) The test statistic is given by,

=

= -3.5/0.7434

= - 4.7081

b) Since the alternative hypothesis is a lower tailed test, the critical region of the test is given by,

, where is the critical value.

Here =0.10. So the critical value of the test is given by,

= - 1.28

Since z = - 4.7081 < - 1.28 = , we ...

#### Solution Summary

The solution contains a Paired Difference Test and the determination of the confidence interval for the mean difference.