Question

A poll asked for people's opinion on whether closing local newspapers would hurt civic life; 427 of 1005 respondents said it would hurt civic life a lot. Complete parts a through d below. Find the proportion of the respondents who said that closing local papers would hurt civic life a lot. (Round to three decimal places as needed.) Find a 95% confidence interval for the population proportion who believed closing newspapers would hurt civic life a lot. Assume the poll used a simple random sample (SRS). (In fact, it used random sampling, but a more complex method than SRS.) (Round to three decimal places as needed.) Find an 80% confidence interval for the population proportion who believed closing newspapers would hurt civic life a lot. (Round to three decimal places as needed.) Which interval is wider and why? The 95% interval is wider. To get a higher degree of certainty, the interval needs to be widened just on the left side. The 80% interval is wider. To get a higher degree of certainty, the interval needs to be widened. The 95% interval is wider. To get a higher degree of certainty, the interval needs to be widened. The 95% interval is wider. To get a higher degree of certainty, the interval needs to be widened just on the right side.

Answer 1

Answer:

A. 0.4249

B. 95% CI = 0.4248-0.031 < p < 0.4249+0.030

C. 80% CI = 0.4249-0.0198 < p < 0.4249+0.0198

D.95% CI is wider than 80% CI.

The more confidence you want, the wider the CI must be.

Step-by-step explanation:

Poll asked for people's opinion on whether closing local newspapers would hurt civic life; 427 of 1005 respondents said it would hurt civic life a lot.

A.The proportion of the respondents who said closing local papers would hurt civic life a lot. (round to three decimal places as needed)

427/1005 = 0.4249

B. The 95% confidence interval for the population proportion who believed closing newspaper would hurt civic life a lot. Assume the poll used a simple random sample (SRS).

Therefore, 1.96√ 0.4249×0.57/1005 = 0.0304

95% CI 0.4248-0.031 < p < 0.4249+0.030

C. 80% confidence interval for the population proportion who believed closing newspapers would hurt civic life a lot.

= 1.2820×√[0.4249×0.57/1005] = 0.0198

80% CI: 0.4249-0.0198 < p < 0.4249+0.0198

D. 95% CI is wider than 80% CI.

The more confidence you want, the wider the CI must be.