7. A public health survey is to be conducted on an inner city area to estimate the proportion of children, ages 0 to 14, having adequate polio immunization.

(a) Out of a sample of 1500 inner-city children in Baltimore, 1125 had received adequate polio immunization.

(i) Compute a two-sided 95% confidence interval estimate for the proportion of Baltimore's inner-city children with adequate polio immunization.

(ii) How large a sample would be required for the total length of a two-sided 95% confidence interval to be 0.03 or less?

(iii) Answer the same question in part (ii) except for Cleveland instead of Baltimore (assuming you have no data for Cleveland).

(b) Out of a sample of 1200 inner-city children in Cleveland, 960 had received adequate polio immunization.

(i) Using a test statistic, test if the proportion of Baltimore's inner-city children with adequate polio immunization is strictly less than the proportion of Cleveland's at the 0.01 level of significance. State your hypotheses.

(ii) What is the p-value of your test?