Question: To test \(H_{0}: \mu=4.5\) versus \(H_{1}: \mu>4.5\), a simple random sample of size \(n=13\) is obtained from a population that is known to be normally distributed.

1. If \(\bar{x}=4.9\) and \(s=1.3\), compute the test statistic.
2. Draw a \(t\) -distribution with the area that represents the \(P\) -value shaded.
3. Approximate and interpret the \(P\) -value.
4. If the researcher decides to test this hypothesis at the \(\alpha=0.1\) level of significance, will the researcher reject the null hypothesis? Why?

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