An international study on executive working hours reported that company CEOs worked more than 60 hours per week on average. The South African Institute of Management (SAIM) wanted to test whether this norm applied to South African CEO's as well.

A random sample of 90 CEO's from South African companies was drawn, and each executive was asked to record the number of hours worked during a given week. The sample mean number of hours worked per week was found to be 61.3 hours. Assume a normal distribution for weekly hours worked and a population standard deviation of 8.8 hours.

Questions: a)Do South African CEO's work more than 60 hours per week on average? Test this claim at the 5% level of significance.

b)Use the p-value method to conduct the hypothesis test for a single population mean.