A computer manufacturer is interested in offering a new model with a state-of-the-art microprocessor that the production department claims has a faster calculation speed than any machine the company sold last year. For years, the CEO has kept in his arsenal a brute force program that commands the machines to find and display the first 10,000 prime numbers (a number evenly divisible only by itself and 1) in a list box on the screen. The first 10 prime numbers are 1, 2, 3, 5, 7, 11, 13, 17, 19, and 23. Last year's fastest computers averaged 4.35 seconds. Sixteen machines, hot off the assembly line and equipped with the new chip, executed the same program. The times (in seconds) that each computer required to list the prime numbers were as follows:
3.65 4.29 3.78 4.21 3.75 3.68 3.71 3.64
3.75 4.03 3.75 4.12 3.73 3.88 3.63 3.59
a. State the appropriate null and alternative hypotheses.
b. find out the test statistic.
c. At  = 0.01, should the CEO reject the null hypothesis?
d. What conclusion can the CEO draw?