Let us consider the following problem. We have a huge amount of data showing that the mean acceleration time (0 to 60 miles per hour) is 10.2 seconds when using regular unleaded gasoline. Now suppose that we make 41 such tests using premium unleaded gasoline because we want to find out whether premium unleaded gasoline gives us a reduction (improvement) in mean acceleration time. The sample mean acceleration for this group turns out to be 9.7 seconds with sample standard deviation of 2.1 seconds. Go to http://davidmlane.com/hyperstat/, an online statistics text, to answer the following problems related to Mr. James's problem. Read Chapter 9: The Logic of Hypothesis Testing and Chapter 10: Testing Hypothesis using Standard Errors. After reading these two Chapters, use your knowledge to answer the following problems:
What is the value of the test statistic for this test using the Z-test?