Administrative staff based at a business school in the UK are advised to take a 15 minute break from their personal computer after working on it for 90 minutes continuously. A random sample of 36 staff revealed that, one average a break was taken after 97.4 minutes of continuous use. The corresponding standard deviation was measured at 5.1 minutes.
a. Provide a 99% confidence interval for the population mean time for working on a PC continuously, prior to taking a break.
b. Conduct a suitable test at the 1% level of significance, to see whether staff, on average, are working longer than advised.