People were polled on how many books they read the previous year. Initial survey results indicate that \(s=18.8\) books.

(a) How many subjects are needed to estimate the mean number of books read the previous year within four books with \(90 \%\) confidence?

(b) How many subjects are needed to estimate the mean number of books read the previous year within two books with \(90 \%\) confidence?

(c) What effect does doubling the required accuracy have on the sample size?

(d) How many subjects are needed to estimate the mean number of books read the previous year within four books with \(99 \%\) confidence? Compare this result to part (a). How does increasing the level of confidence in the estimate affect sample size? Why is this reasonable?