Perform the Indicated Hypothesis Test $$\sigma _ { 1 } ^ { 2 } \leq \sigma { } _ { 2 } ^ { 2 } \text {. }$$

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.
-Test the claim that $$\sigma _ { 1 } ^ { 2 } \leq \sigma { } _ { 2 } ^ { 2 } \text {. }$$ Two samples are randomly selected from populations that are normal. The
sample statistics are given below. Use $$\alpha = 0.05 \text {. }$$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 15 \\\\\mathrm {~s} _ { 1 } ^ { 2 } = 21.866 & \mathrm {~s} _ { 2 } ^ { 2 } = 20.384\end{array}$$