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    Paired Difference Test

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    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.

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    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.