Use the two-proportions z-interval procedure to obtain the required confidence interval for the difference between twopopulation proportions. Assume that independent simple random samples have been selected from the two populations.
-A survey found that 28 of 69 randomly selected women and 41 of 78 randomly selected men follow a regular exercise program. Find a 95% confidence interval for the difference between the
Proportions of women and men who follow a regular exercise program.
A)-0.310 to 0.596
B)0.215 to 0.596
C)0.245 to 0.566
D)-0.280 to 0.040

Question

Use the two-proportions z-interval procedure to obtain the required confidence interval for the difference between twopopulation proportions. Assume that independent simple random samples have been selected from the two populations.
-A survey found that 28 of 69 randomly selected women and 41 of 78 randomly selected men follow a regular exercise program. Find a 95% confidence interval for the difference between the
Proportions of women and men who follow a regular exercise program. 
A)-0.310 to 0.596
B)0.215 to 0.596
C)0.245 to 0.566
D)-0.280 to 0.040

Quizplus · Accepted Answer

The confidence interval for the difference between two proportions ($p_1 - p_2$) can be calculated using the formula: $$CI = (\hat{p}_1 - \hat{p}_2) \pm z * \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$$ where $\hat{p}_1$ and $\hat{p}_2$ are the sample proportions, $n_1$ and $n_2$ are the sample sizes, and $z$ is the z-score corresponding to the desired level of confidence (for 95% confidence, $z \approx 1.96$). For women, $\hat{p}_1 = 28/69$, and for men, $\hat{p}_2 = 41/78$. Plugging these values into the formula gives a confidence interval that suggests the difference between the proportions of women and men who follow a regular exercise program could include zero, indicating there might not be a significant difference between the two proportions. This matches choice D, which is the only interval that spans zero.

Use the Two-Proportions Z-Interval Procedure to Obtain the Required Confidence