In a random sample of 500 California residents,350 indicated that they were home owners.In another random sample of 700 Florida residents,455 indicated that they were home owners.What is the 99% confidence interval for the difference between the proportions?
A)0.05 ± 0.070
B)0.05 ± 0.085
C)0.05 ± 0.053
D)0.05 ± 0.045

Question

Quizplus · Accepted Answer

The correct answer is A because the 99% confidence interval for the difference between the proportions is 0.05 ± 0.070. This can be calculated using the formula:CI = (p1 - p2) ± z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))where p1 is the proportion of home owners in the first sample, p2 is the proportion of home owners in the second sample, n1 is the sample size of the first sample, n2 is the sample size of the second sample, and z is the z-score corresponding to the desired confidence level.In this case, p1 = 350/500 = 0.7, p2 = 455/700 = 0.65, n1 = 500, n2 = 700, and z = 2.576 (for a 99% confidence level). Plugging these values into the formula, we get:CI = (0.7 - 0.65) ± 2.576 * sqrt((0.7 * (1 - 0.7) / 500) + (0.65 * (1 - 0.65) / 700))= 0.05 ± 0.070

In a Random Sample of 500 California Residents,350 Indicated That