The production department at Greenside Corporation, a manufacturer of lawn equipment, has devised a new manual assembly method for its lawn tractors. Now it wishes to determine if it is reasonable to conclude the mean assembly time of the new method is less than the old method. Accordingly, they have randomly sampled assembly times from 40 tractors using the old method and 32 tractors using the new method. A portion of the data is shown in the accompanying table.
Old Method Times (Minutes) New Method Times (Minutes)
32...........................................................30
36...........................................................32
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a. Set up the hypotheses to test the claim that the mean assembly time using the new method is less than the old method.
b. Using the appropriate commands in Excel, find the value of the test statistic and the p-value. Assume the population variances are unknown and not equal.
c. At the 5% significance level, what is the conclusion? What if the significance level is 10%?