In a study of computer use, 1,000 randomly selected Canadian Internet users were asked how much time they spend online in a typical week (Ipsos Reid, August 9, 2005). The sample mean was 12.7 hours.
a. The sample standard deviation was not reported, but suppose that it was 5 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent online by Canadians in a typical week is greater than 12.5 hours.
b. Now suppose that the sample standard deviation was 2 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent online by Canadians in a typical week is greater than 12.5 hours.
c. Explain why the null hypothesis was rejected in the test of Part (b) but not in the test of Part (a).