In a recent survey of gun control laws, a random sample of 564 women, 313 favored stricter gun control laws. In a random sample of 588 men, 307 favored stricter gun control laws. Can it be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women? What is the value of the test statistic?
$-1.12$
1.47
0.24

Step 1 ：We are given two samples, one of women and one of men, and we are asked to test if the proportion of men who favor stricter gun control laws is less than the proportion of women who do the same.

Step 2 ：The null hypothesis (H0) is that the proportions are equal, i.e., P1 = P2, where P1 is the proportion of women who favor stricter gun control laws and P2 is the proportion of men who favor stricter gun control laws.

Step 3 ：The alternative hypothesis (H1) is that the proportion of men who favor stricter gun control laws is less than the proportion of women, i.e., P1 > P2.

Step 4 ：We can use the formula for the test statistic in the hypothesis testing for two proportions, which is: \(Z = \frac{P1 - P2}{\sqrt{P(1 - P) * [(1/n1) + (1/n2)]}}\), where P is the pooled sample proportion, calculated as: \(P = \frac{x1 + x2}{n1 + n2}\), where x1 and x2 are the number of 'successes' (people favoring stricter gun control laws) in each sample, and n1 and n2 are the sizes of the samples.

Step 5 ：Given that n1 = 564, x1 = 313, n2 = 588, x2 = 307, we calculate p1 = 0.5549645390070922, p2 = 0.5221088435374149, p = 0.5381944444444444.

Step 6 ：Substituting these values into the formula, we get \(Z = 1.1181844750391814\).

Step 7 ：The calculated test statistic is approximately 1.12. This is the value we will compare to the critical value to decide whether to reject the null hypothesis.

Step 8 ：The critical value for a one-tailed test at the .05 level of significance is approximately 1.645. Since our calculated test statistic is less than the critical value, we do not reject the null hypothesis.

Step 9 ：Therefore, we cannot conclude at the .05 level of significance that a lower proportion of men favor stricter gun control than women.

Step 10 ：Final Answer: The value of the test statistic is approximately \(\boxed{1.12}\).