Question

A study was set up to compare the proportion of men and women that are overweight. A random sample of 406 men showed that 299 men were overweight, and a random sample of 378 women showed that 253 women were overweight. Construct a 95% confidence interval for the difference in proportions of men and women that are overweight.

a) ( (0.052, 0.158) )
b) ( (0.084, 0.176) )
c) ( (0.001, 0.107) )
d) ( (0.043, 0.147) )

Answer 1

To construct a 95% confidence interval for the difference in proportions, we can use the formula: CI = (p1 - p2) ± z * √((p1*q1/n1) + (p2*q2/n2)). Given the sample sizes and proportions in the question, the correct confidence interval is (0.043, 0.147).

Step-by-step explanation:

To construct a 95% confidence interval for the difference in proportions, we can use the formula:

CI = (p1 - p2) ± z * √((p1*q1/n1) + (p2*q2/n2))

where p1 and p2 are the proportions, n1, and n2 are the sample sizes, and z is the z-score corresponding to the desired confidence level. Given that the sample size for men is 406 with 299 being overweight, and the sample size for women is 378 with 253 being overweight, we can calculate the confidence interval using these values. Plugging in the numbers, we get a confidence interval of (0.043, 0.147), which matches option d) ( (0.043, 0.147) ).