For this problem, carry at least four digits after the decimal in your calculati

Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding 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 , how large a sample is necessary to be 98% sure that a point estimate p will be within a distance of 0.11 from p? (Round your answer up to the nearest whole number.) small businesses (b) In a preliminary random sample of 30 small businesses, it was found that seven had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be 98% sure that a point estimate p will be within a distance of 0.110 from p? (Round your answer up to the nearest whole number.) more small businesses

Explanation / Answer

a) here for no preliminary point estimate p=0.5

for 98% CI ; z=2.326

margin of error E =0.11

hence sample size n=p(1-p)*(Z/E)2 =~112

b) here point estimate p=0.2333

hence sample size n=p(1-p)*(Z/E)2 =~81

hence number of small business to be added =81-30=51

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