An electronics manufacturing process has a scheduled mean completion time of 65 minutes. It is claimed that, under new management, the mean completion time, ?, is less than 65 minutes. To test this claim, a random sample of 12 completion times under new management was taken.

The sample had a mean completion time of 57 minutes and a standard deviation of 12 minutes. Assume that the population of completion times under new management is normally distributed. At the 0.05 level of significance, can it be concluded that the mean completion time, ?, under new management is less than the scheduled mean?

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

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

(a) State the null hypothesis / and the alternative hypothesis H. P H : I X S p H , : 0 (b) Determine the type of test statistic to use. Degrees of freedom: I 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0+0 00 X ? (d) Find the p-value. (Round to three or more decimal places.) (e) At the 0.05 level, can it be concluded that the mean completion time under new management is less than the scheduled mean? Yes No