# Hypothesis Test - Paired Samples

In a two-population test, when will you use paired samples?

Provide an example and state the Null and the Alternative hypothesis for the examples in symbolic form.

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#### Solution Preview

In a two-population test, paired samples are used when measurements are taken from the same subject before and after making some changes or manipulations in them. Two-sample hypothesis test for paired samples can also be used to compare samples that are subjected to different conditions, provided the samples in each pair are identical. For example, when a particular parameter is measured from the same person by subjecting him to a pre-test and a post-test and the results are compared.

Let us consider the following ...

#### Solution Summary

This solution sets out the hypothesis, sample mean and standard deviation; and using the sample data conducts a paired sample t-test to test the null hypothesis. The solution then determines the degrees of freedom, the critical value, the decision rule, the standard deviation of the differences, the standard error, the t-statistic, and the p-value. An interpretation of the results is discussed. This solution is provided in an attached Word document.