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.
-In a random sample of 45 Democrats from one city, 10 approved of the mayor's performance. In a random sample of 49 Republicans from the city, 24 approved of the mayor's performance. Find a
90% confidence interval for the difference between the proportions of Democrats and Republicans
Who approve of the mayor's performance.
A)-0.423 to -0.112
B)0.037 to 0.408
C)0.035 to 0.408
D)0.065 to 0.379

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.
-In a random sample of 45 Democrats from one city, 10 approved of the mayor's performance. In a random sample of 49 Republicans from the city, 24 approved of the mayor's performance. Find a
90% confidence interval for the difference between the proportions of Democrats and Republicans
Who approve of the mayor's performance. 
A)-0.423 to -0.112
B)0.037 to 0.408
C)0.035 to 0.408
D)0.065 to 0.379

Quizplus · Accepted Answer

The confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance is calculated using the formula for a two-proportion z-interval. The sample proportions are $p_1 = \frac{10}{45}$ for Democrats and $p_2 = \frac{24}{49}$ for Republicans. The confidence interval formula incorporates these sample proportions, the sample sizes, and the z-score corresponding to the desired confidence level (90% in this case). The calculation results in a confidence interval that suggests the proportion of Republicans approving the mayor's performance is higher than that of Democrats, with the interval entirely below 0, indicating the difference is negative (Republicans' approval rate is higher). The correct interval is -0.423 to -0.112, which means the difference in approval rates (Republican - Democrat) lies within this range with 90% confidence.

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