A new model of Sun workstation is being considered for purchase. The com pany is willing to consider purchasing the new model only if it results in faster computing times. The average time for a particular kind of program on the current computer is 35 seconds.
(a) A random sample of 38 runs with the new model results in an average time of 33 seconds with a standard deviation of 5 seconds. Perform the desired hypothesis test by computing a p-value.
(b) How large a sample size would be needed to conduct the test in part
(a) at level o: = 0.05 and have a power of 0.8 for detecting a difference from the null value (35 seconds) of 0.4a-?