Question: To test \(H_{0}: \mu=80\) versus \(H_{1}: \mu<80\), a simple random sample of size \(n=22\) is obtained from a population that is known to be normally distributed.

1. If \(\bar{x}=76.9\) and \(s=8.5\), compute the test statistic.
2. If the researcher decides to test this hypothesis at the \(\alpha=0.02\) level of significance, determine the critical value.
3. Draw a \(t\) -distribution that depicts the critical region.
4. Will the researcher reject the null hypothesis? Why?

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