For this problem, carry at least four digits after the decimalin your calculations. Answers may vary slightly due torounding.
The National Council of Small Businesses is interested in theproportion of small businesses that declared Chapter 11 bankruptcylast year. Since there are so many small businesses, the NationalCouncil intends to estimate the proportion from a random sample.Let p be the proportion of small businesses that declaredChapter 11 bankruptcy last year.
(a) If no preliminary sample is taken to estimate p,how large a sample is necessary to be 99% sure that a pointestimate p̂ will be within a distance of 0.09 fromp? (Round your answer up to the nearest wholenumber.)
small businesses
(b) In a preliminary random sample of 30 small businesses, it wasfound that thirteen had declared Chapter 11 bankruptcy. How manymore small businesses should be included in the sample tobe 99% sure that a point estimate p̂ will be within adistance of 0.090 from p? (Round your answer up to thenearest whole number.)
more small businesses
