Question

Are you likely to purchase an item promoted by a celebrity on a social media​ site? According to a​ survey, 26​% of social media users have made such a purchase. Complete parts​ (a) through​ (d) below.

a. Suppose that the survey had a sample size of nequals1000. Construct a 90 % confidence interval estimate for the population proportion of social media users that have purchased an item promoted by a celebrity on a social media site. nothingless than or equalspiless than or equals nothing ​(Type an integer or a decimal. Round to four decimal places as​ needed.)

b. Based on​ (a), can you claim that more than a quarter of all social media users have purchased an item promoted by a celebrity on a social media​ site?

choose correct answer below

A. ​No, because a 90 % confidence interval is not indicative of a guarantee. A​ 99.9% confidence interval would be needed to make such a claim.

B. ​Yes, with 90 % confidence because the sample proportion is greater than a​ quarter, and it falls within the limits of the confidence interval estimate.

C. ​Yes, with 90 % confidence because all the values contained in the confidence interval are greater than 0.25.

D. ​No, because the confidence interval contains proportion values that are less than 0.25.

c. Repeat parts​ (a) and​ (b), assuming that the survey had a sample size of n equals 11,000. Construct a 90 % confidence interval estimate for the population proportion of social media users that have purchased an item promoted by a celebrity on a social media site. nothing less than or equals pi less than or equals nothing ​(Type an integer or a decimal. Round to four decimal places as​ needed.)

Based on the confidence interval created using a sample size of 11,000​, can you claim that more than a quarter of all social media users have purchased an item promoted by a celebrity on a social media​ site?

choose correct answer below

A. ​No, because the confidence interval contains proportion values that are less than 0.25.

B. ​No, because a 90 % confidence interval is not indicative of a guarantee. A​ 99.9% confidence interval would be needed to make such a claim.

C. ​Yes, with 90 % confidence because the sample proportion is greater than a​ quarter, and it falls within the limits of the confidence interval estimate.

D. ​Yes, with 90 % confidence because all the values contained in the confidence interval are greater than 0.25.

d. Discuss the effect of sample size on confidence interval estimation.

Choose the correct answer below.

A. A larger sample size has no effect on a confidence​ interval, holding everything else constant.

B. A larger sample size results in a narrower confidence​ interval, holding everything else constant.

C. A larger sample size results in a wider confidence​ interval, holding everything else constant.

D. It is impossible to compare confidence interval estimates with difference sample sizes because the sample size is part of the formula for finding confidence interval estimate limits.

Answer 1

Here we have 0.26 + .645 X0261-026) し000 -0.26 ± .0228 Conbins mport% n Nor bec rnee contf dona_.inkrva) リ000 0.26 ±0.00 63