3a. The potato farmers in Wilson County are concerned about possible crop damage due to the spotted beetle. Agricultural officials in the county have sampled 25 different 1 acre lots at random and have determined from the sample an average of 3000 beetles per acre with a sample standard deviation of 780 beetles. The officials are going to construct a 95% confidence interval for the population mean.

(i) What assumption has to make in the construction of the 95% confidence interval? (6 marks)

(ii) Construct the 95% confidence interval for the population means. (10 marks)

b. The management of a university is considering raising tuition to improve school facilities, and the management wants to determine what percentage of students favoring the increase. The management needs to be 90% confident that the percentage has been estimated to within +/- 3% of the true value. How large a sample is needed to guarantee this accuracy regardless of the true percentage?