A researcher is interested in estimating the difference in two population proportions.A sample of 400 from each population results in sample proportions of .61 and .64.A 90% confidence interval for the difference in the population proportions is _______.
A)-0.10 to 0.04
B)-0.09 to 0.03
C)-0.11 to 0.05
D)-0.07 to 0.01
E)-0.08 to 0.12

Question

Quizplus · Accepted Answer

To estimate the difference in two population proportions with a confidence interval, we use the formula for the confidence interval of two proportions: $\hat{p}_1 - \hat{p}_2 \pm Z * \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$, where $\hat{p}_1$ and $\hat{p}_2$ are the sample proportions, and $n_1$ and $n_2$ are the sample sizes. Given $\hat{p}_1 = 0.61$, $\hat{p}_2 = 0.64$, and $n_1 = n_2 = 400$, and using a Z value for a 90% confidence interval (which is approximately 1.645), we calculate the confidence interval. The calculation results in a confidence interval of approximately -0.09 to 0.03, which matches choice B.

A Researcher Is Interested in Estimating the Difference in Two