In a sample of 54 men, 33 said that they had less leisure time taday than they had 10 years ago. in a sample of 54 wamen, 43 wamen said that they had less leisure bine today than they had 10 years ago. At $a=0.05$, is there a difference in the proportions?

Use $p_{1}$ for the proportion of men with less lessure time.
Part 1 of 6
State the hypotheses and identify the claim with the correct hypothesis.
\[
\begin{array}{l|l|l|}
H_{0}+p_{1}=p_{2} & \text { not daim } \\
H_{1}=P_{1} \neq p_{2} & \text { daim } & +
\end{array}
\]

This hypothesis test is a bwo-tailed $\mathbf{v}$ test.

Part: 1 / 6

Part 2 of 5
Find the critical value(s), Round the answer (s) to teo deconal places, if there is more than one criticat value, separate them with cominas:
\[
\text { Criticit valuets): } \square
\]

Step 1 ：State the hypotheses and identify the claim with the correct hypothesis. The null hypothesis \(H_{0}: p_{1}=p_{2}\) is not the claim. The alternative hypothesis \(H_{1}: p_{1} \neq p_{2}\) is the claim. This hypothesis test is a two-tailed test.

Step 2 ：Find the critical value(s). The test statistic for this hypothesis test follows a standard normal distribution because we are dealing with proportions. The critical value(s) can be found using the standard normal distribution table for a significance level of 0.05. Since this is a two-tailed test, we need to find the critical values for both tails of the distribution.

Step 3 ：Calculate the critical values. For a significance level of 0.05, the critical values for a two-tailed test are approximately -1.96 and 1.96. These are the values that the test statistic must exceed in order to reject the null hypothesis.

Step 4 ：The final answer: The critical values are \(\boxed{-1.96, 1.96}\).