A study reports that senior citizens who get regular exercise experience fewer symptoms of depression. Analyze the following hypothetical results:

Solution: We have the following table:

We are interested in testing

which corresponds to a left-tailed independent samples t-test. Since we assume that the variances are equal, the t-statistics is computed as:

where the pooled standard deviation is computed as

This means that the t-statistics is

The critical values for this two-tailed test are, and the rejection region is therefore

Since we have that <, then we reject the null hypothesis.

This means that we have enough evidence to support the claim that senior citizens who get regular exercise experience fewer symptoms of depression, at the 0.05 significance level.

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