Question

A survey reported in Time magazine included the question Do you favor a federal law requiring a 15 day waiting period to purchase a gun?" Results from a random sample of US citizens showed that 318 of the 520 men who were surveyed supported this proposed law while 379 of the 460 women sampled said yes". Use this information to find a 95% confidence interval for the difference in the two proportions, Pm-Pw , where Pm is the proportion of men who support the proposed law and Pw is the proportion of women who support the proposed law.

Answer 1

To find a 95% confidence interval for the difference in the two proportions, Pm-Pw, we can use the formula: CI = (Pm - Pw) ± Z * sqrt((Pm * (1 - Pm)) / nm + (Pw * (1 - Pw)) / nw). Plugging in the values, the 95% confidence interval for the difference in proportions is (-0.293, -0.131).

Step-by-step explanation:

To find a 95% confidence interval for the difference in the two proportions, Pm-Pw, we can use the formula:

CI = (Pm - Pw) ± Z * sqrt((Pm * (1 - Pm)) / nm + (Pw * (1 - Pw)) / nw)

Where:

Pm = proportion of men who support the proposed law

Pw = proportion of women who support the proposed law

Z = Z-score corresponding to the desired confidence level (in this case, 95%)

nm = sample size of men

nw = sample size of women

Using the given information:

Pm = 318/520 ≈ 0.612

Pw = 379/460 ≈ 0.824

nm = 520

nw = 460

Using a Z-score table or calculator, we find that the Z-score for a 95% confidence level is approximately 1.96.

Plugging in the values:

CI = (0.612 - 0.824) ± 1.96 * sqrt((0.612 * (1 - 0.612)) / 520 + (0.824 * (1 - 0.824)) / 460)

Simplifying the expression:

CI = -0.212 ± 1.96 * sqrt(0.000944 + 0.000764)

CI = -0.212 ± 1.96 * sqrt(0.001708)

CI = -0.212 ± 1.96 * 0.041324

CI = -0.212 ± 0.081

CI = (-0.293, -0.131)

Therefore, the 95% confidence interval for the difference in proportions, Pm-Pw, is (-0.293, -0.131).