Chapter 8.3, Problem 26P

Small Business: Bankruptcy The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year.

(a) If no preliminary sample is taken to estimate p. how large a sample is necessary to be $95\%$ sure that a point estimate $\hat{p}$ will be within a distance of 0.10 from p?

(b) In a preliminary random sample of 38 small businesses, it was found that six had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be $95\%$ sure that a point estimate $\hat{p}$ will be within a distance of 0.10 from p?