A new operating system is installed in every workstation at a large company. The claim of the operating system manufacturer is that the time to shut down and turn on the machine will be much faster. To test it an employee selects 36 machines and tests the combined shut down and restart time of each machine before and after the new operating system has been installed. The mean and standard deviation of the differences (before – after) is 23.5 seconds with a standard deviation of 40 seconds.
a) What is the standard error of the mean difference?
b) How many degrees of freedom does the t-statistic have?
c) What is the 90% confidence interval for the mean difference?
d) What do you conclude at α = 0.05?