Perform the Indicated Hypothesis Test $$\alpha = 0.01$$

Essay

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
-A statistics teacher believes that the variance of test scores of students in her evening statistics class is lower
than the variance of test scores of students in her day class. The results of an exam, given to the day and
evening students, are shown below. Can the teacher conclude that the scores of evening students have a lower
variance? Use $$\alpha = 0.01$$ $$\begin{array} {cc } \text { Day Students}& \text { Evening Students}\\\mathrm { n } _ { 1 } = 31 & \mathrm { n } _ { 2 } = 41 \\\\\mathrm {~s} _ { 1 } = 9.8 & \mathrm {~s} _ { 2 } = 5.3\end{array}$$