Professional pollsters are concerned with the growing proportion of refusals among potential survey subjects. Apriori suppose pollsters believe that the refusal rate is somewhere between 20% to 30%.
a) How large a sample do you need for the sample proportion to have a margin of error of (plus/minus) 3% at the 95% confidence level? Assume DeMoivre Approximation is valid.
(I know this is a rather simple equation to plug into, but don't remember.)
b) Suppose among 312 large city residents sampled, 65 refused to cooperate. What is the margin of error at the 95% confidence level. Assume DeMoivre is v valid again.
c) Pollsters are interested in knowing if the refusal rate is universal or differs according to the community in which the subjects live. To test if there is a difference between city dwellers and rural residents, a study was done. The results for city dwellers is found to in part (b) above and 51 refused to cooperate among 197 rural residents. Set up hypotheses and test at the 5% significance level to decide if there is a difference in the proportion of refusals in these two communities.