Installation of a certain hardware takes random time with a standard deviation of 5 minutes. (a) A computer technician installs this hardware on 64 different computers with an average installation time of 42 minutes. Compute a 95% confidence interval for the mean installation time.
(b) Suppose that the population mean installation time is 40 minutes. A technician installs the hardware on your PC. What is the probability that the installation time will be within the interval computed in (a)?
(c) A manager questions the assumption of the above. Her pilot sample of 40 installation times has a sample standard deviation of s = 6.2 min, and she says that it is significantly different from the assumed value of standard deviation = 5 min. Do you agree with the manager? Conduct a suitable test of a standard deviation.