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.
$$\overline{)\begin{array}{ll}{H}_0+p_1=p_2& \text{ not daim }\\ H_1=P_1\ne p_2& \text{ daim }& +\end{array}}$$

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:
$$\text{ Criticit valuets): }◻$$

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 $H_1:p_1\ne p_2$ 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 $\boxed{{\displaystyle -1.96,1.96}}$.