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An electronics manufacturing process has historically had a mean completion time of 65 minutes. It is claimed that, due to improvements in the process, the mean completion time, µ, is now less than 65 minutes. A random sample of 18 completion times using the new process is taken. The sample has a mean completion time of 59 minutes, with a standard deviation of 11 minutes.

Assume that completion times using the new process are approximately normally distributed. At the 0.05 level of significance, can it be concluded that the population mean completion time using the new process is less than 65 minutes?

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

Carry your intermediate computations to three or more decimal places.

(a) State the null hypothesis H^0, and the alternative hypothesis H^1
(b) Determine the type of test statistic to use. (Choose one)
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the P-value. (Round to three or more decimal places.)
(e) Can it be concluded that the mean completion time using the new process in less than 65 minutes?

Sagot :

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