A survey is conducted to compare public attitudes towards local policing. A number of people in two areas of interest are sampled, and asked if they are satisfied with their local police-community relationship. The results of this survey are shown in the following table.

Sample size Number satisfied

Area A 153 115

Area B 188 120

(a) You are asked to consider an appropriate hypothesis test to determine whether there is a difference between the two areas in the proportion who are satisfied. Test at two appropriate significance levels and comment on your findings. Specify the test statistic you use and its distribution under the null hypothesis.

(b) Compute a 98% confidence interval for the proportion of people in Areas A and B combined who are satisfied, assuming the respective sample sizes are proportional to population sizes.