Question

A medical researcher wishes to determine the percentage of females who take vitamins. He wishes to be 99% confident that the estimate is within 2 percentage points of the true proportion. a) If no estimate of the sample proportion is available, how large should the sample be?

b) A recent study showed that 25% of females take vitamins. Given this additional information, how large a sample size would be needed?

c) Compare the results in a) and b) and comment on the effect on the sample size of having additional information.

Answer 1

a) At 99% confidence interval the critical value is z_0.005 = 2.575

Margin of error = 0.02

Or, z_0.005 * sqrt(p(1 - p)/n) = 0.02

Or, 2.575 * sqrt(0.5 * 0.5/n) = 0.02

Or, n = (2.575 * sqrt(0.5 * 0.5)/0.02)^2

Or, n = 4145

b) Margin of error = 0.02

Or, z_0.005 * sqrt(p(1 - p)/n) = 0.02

Or, 2.575 * sqrt(0.25 * 0.75/n) = 0.02

Or, n = (2.575 * sqrt(0.25 * 0.75)/0.02)^2

Or, n = 3109

C) The sample size for (a) is larger than the sample for (b).

The sample size for no preliminary estimate is larger than for the sample size of preliminary estimate.