A. Suppose a hospital would like to estimate the proportion of patients who feel that physicians who care for them always communicated effectively when discussing their medical care. A pilot sample of 40 patients found that 24 reported that their physician communicated effectively. Determine the additional number of patients that need to be sampled to construct a 90​% confidence interval with a margin of error equal to 8​% to estimate this proportion. The additional number of patients that need to be sampled is __? (Round up to the nearest​ integer.)

B.

A tire manufacturer would like to estimate the average tire life of its new​ all-season light truck tire in terms of how many miles it lasts. Determine the sample size needed to construct a 98​% confidence interval with a margin of error equal to 2,700 miles. Assume the standard deviation for the tire life of this particular brand is 7,000 miles. The sample size needed is _? ​(Round up to the nearest​ integer.)

C.

A certain region would like to estimate the proportion of voters who intend to participate in upcoming elections. A pilot sample of 50 voters found that 28 of them intended to vote in the election. Determine the additional number of voters that need to be sampled to construct a 92​% interval with a margin of error equal to 0.06 to estimate the proportion. The region should sample __? additional voters. ​(Round up to the nearest​ integer.)

D.

Determine the sample size n needed to construct a 95​% confidence interval to estimate the population proportion for the following sample proportions when the margin of error equals 5​%.

I. p=0.20

II. p=0.30

III. p=0.40