An automobile assembly line operation has a scheduled mean completion time,, of14.2 minutes. The standard deviation of completion times is1.7 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of60 completion times under new management was taken. The sample had a mean of13.6 minutes. Can we support, at the0.01 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed.

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult alist of formulas.)

(a)State the null hypothesisH0 and the alternative hypothesisH1.

H0:

H1:

(b)Determine the type of test statistic to use.

(c)Find the value of the test statistic.

(d)Find thep-value.

(e)Can we support the claim that the mean completion time has decreased under new management?YesNo