Question

The national council onsmall buisnesses is interested i the proportion of small buisnesses that declared Chapter 11 bankruptcy last year. Since there are so many small buisnesses, the national council intends to estimate the proportion from a random sample. Let p be the proportion of small buisjesses 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 p^ will be within a distance of 0.12 from p?

(b) In a preliminary random sample of 30 small buisnesses, it was found that ten had declared chapter 11 bankruptcy. How many more small buisnesses should be included in the sample to be 95% sure that a point estimate p^ will be within a distance of 0.120 from p?

Answer 1