Question

In each​ case, find the approximate sample size required to construct a 90​% confidence interval for p that has sampling error SE=0.03.

a. Assume that p is near 0.2

b. Assume that you have no prior knowledge about​ p, but you wish to be certain that your sample is large enough to achieve the specified accuracy for the estimate.

Answer 1

Given : The samplig error is , SE=0.03

The significance level is ,

Now , ; From Z-table

Therefore , the margin of error is ,

a. Since ,

Therefore , the required sample size is ,

b. Since , there is no prior knowledge about p.

Now , assume that

Therefore , the required sample size is ,