a. Estimating p and Consider randomly selecting a sample of n measurements without replacement from a

a. Estimating p and г
Consider randomly selecting a sample of n measurements without replacement from a finite population consisting of N measurements and having variance σ2. Also consider the sample size given by the formula

Then, it can be shown that this sample size makes the margin of error in a 100(1 - α) percent confidence interval for p equal to E if we set D equal to (E/zα/2)2. It can also be shown that this sample size makes the margin of error in a 100(1 - a) percent confidence interval for г equal to E if we set D equal to [E/(zα/2N)]2. Now consider Exercise 8.55. Using s2 = (1.26)2, or 1.5876, as an estimate of σ2, determine the sample size that makes the margin of error in a 95 percent confidence interval for the total number of person-days lost to unexcused absences last year equal to 100 days.
b. Estimating p and г
Consider randomly selecting a sample of n units without replacement from a finite population consisting of N units and having a proportion p of these units fall into a particular category. Also, consider the sample size given by the formula

It can be shown that this sample size makes the margin of error in a 100(1 - α) percent confidence interval for p equal to E if we set D equal to (E/zα/2)2. It can also be shown that this sample size makes the margin of error in a 100(1 - α) percent confidence interval for r equal to E if we set D equal to [E/(zα/2N)2. Now consider Exercise 8.54. Using = .31 as an estimate of p, determine the sample size that makes the margin of error in a 95 percent confidence interval for the proportion of the 1,323 vouchers that were filled out incorrectly equal to .04.

Transcribed Image Text:

No (N-1)D + σ ns