Professional pollsters are concerned with the growing proportion of refusals among potential survey subjects.  Apriority suppose pollsters believe that the refusal rate is somewhere between 20 % to 30%

a. How large a sample do you need for X/n, the sample proportion, to have a margin of error of ±3% at the 95% confidence level?

b. Suppose among 312 large city residents sampled, 65 refused to cooperate.  What is the margin of error at the 95% confidence level.

c. Pollster are interested in knowing if the refusal rate is universal or differs according 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 are found 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's a difference in the proportion of refusals in these two communities.