Question

A state legislator wishes to survey residents of her district to see what proportion of the electorate is aware of her position on using state funds to pay for abortions. (Round your answers up to the nearest integer.) (a) What sample size is necessary if the 95% CI for p is to have a width of at most 0.11 irrespective of p? (b) If the legislator has strong reason to believe that at least 5 6 of the electorate know of her position, how large a sample size would you recommend to maintain a width of at most 0.11? You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

a) For a confidence interval width of 0.11, the margin of error is given as: MOE = 0.11 / 2 = 0.055

From standard normal tables, we have:
P(-1.96 < Z < 1.96) = 0.95

Therefore the margin of error here is obtained as:

Therefore the sample size here is obtained as:

Note that as we dont have a prior proportion value here, we use p = 0.5 to get a conservative value of the sample size here.

Therefore 318 is the required sample size here.

b) Here, we are given the prior proportion value as (5/6), therefore the sample size here is computed as:

Therefore 177 is the required sample size here.