Aresearcher wishes to estimate the percentage of adults who support abolishing the penny. what size sample should be obtained if he wishes the estimate to be within 44 percentage points with 9999% confidence if (a) he uses a previous estimate of 2222%? (b) he does not use any prior estimates?

1.       If he uses a previous estimate of 22%

The problem states within 2 percentage points so the error is 0.02. The z score for this is 2.575.

The solution would be: 0.22(1-0.22) (2.575/0.02)^2 = 0.1716 (16576.5625) = 2844.538125; therefore we need to round up and the sample size would be 2845.

2.       If he does not use any prior estimates.

The sample size required to obtain 1 – α * 100% confidence interval for p with a margin of error E, without a previous estimate of p, is given by: n = 0.25 (z α/2 divided by E) ^2

Therefore, n = 0.25 (2.575/0.02)^2

= 0.25 (16576.5625)

=4144.14; but we need to round up. So the sample size is 4145.