# A study reports that senior citizens who get regular exercise experience fewer symptoms of depression

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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