A survey of the audience at a popular comedian's show in Brisbane's Queensland Performing Arts Centre (QPAC) has been conducted and found that 42 of the 278 members of the audience who participated in the survey are visitors to Brisbane.

(a) Calculate a 95% confidence interval for the proportion of audience members at the comedian's show who are visitors to Brisbane. Present your work.

(b) Interpret the confidence interval.

(c) To conduct a new follow-up study that would provide 95% confidence that the point estimate is correct to within0.03 of the population proportion, how large a sample size is required?

(d) To conduct a a new follow-up study that would provide 99% confidence that the point estimate is correct to within0.03 of the population proportion, how large a sample size is required?