Question: A STATISTIC instructor is interested in whether there is any variation in the final exam grades between her two classes Data collected from the two classes are as follows:

Her null hypothesis and alternative hypothesis are:

\({{H}_{0}}:\sigma _{1}^{2}=\sigma _{2}^{2}\) and \({{H}_{A}}:\sigma _{1}^{2}<\sigma _{2}^{2}\)

1. Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
2. Determine the p-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.
3. Is there sufficient evidence to justify the rejection of H 0 at the 0.01 level? Explain.

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