Question

Background info: In 2003 and 2017 a poll asked Democratic voters about their views on the FBI. In​ 2003, 49​% thought the FBI did a good or excellent job. In​ 2017, 73​% of Democratic voters felt this way. Assume these percentages are based on samples of 1300 Democratic voters.

Construct a 95​% confidence interval for the difference in the proportions of Democratic voters who believe the FBI is doing a good or excellent​ job, p1−p2. Let p1 be the proportion of Democratic voters who felt this way in 2003 and p2 be the proportion of Democratic voters who felt this way in 2017.
The 95​% confidence interval is ___ and ____

Answer 1

To construct a 95% confidence interval for the difference in the proportions of Democratic voters who believe the FBI is doing a good or excellent job, use the formula CI = (p1 - p2) ± z * sqrt((p1 * (1-p1))/n1 + (p2 * (1-p2))/n2), where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and z is the z-score for the desired confidence level. Given the specific values provided in the question, the 95% confidence interval for the difference in proportions is (0.177, 0.233).

Step-by-step explanation:

To construct a 95% confidence interval for the difference in the proportions of Democratic voters who believe the FBI is doing a good or excellent job, we can use the formula:

CI = (p1 - p2) ± z * sqrt((p1 * (1-p1))/n1 + (p2 * (1-p2))/n2)

Where:

• p1 and p2 are the sample proportions
• n1 and n2 are the sample sizes
• z is the z-score for the desired confidence level

Given that the sample proportions are 49% and 73% for 2003 and 2017 respectively, and the sample sizes are 1300 for both years, we can now calculate the confidence interval.

Using a z-score of 1.96 for a 95% confidence level, the 95% confidence interval for the difference in proportions is (0.177, 0.233).