Question

An electronics manufacturing process has a scheduled mean completion time of 75 minutes. It is claimed that, under new management, the mean completion time, H, is less than 75 minutes. To test this claim, a random sample of 15 completion times under new management was taken. The sample had a mean completion time of 70 minutes and a standard deviation of 9 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, I, under new management is less than the scheduled mean? Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. o The ul hypothesis H:0 5 The tematice hypothesis: Do - Os The type of best statistic Choose) - DD The value of the tests: (Round to at least three omal places) X 5 2 The the 0.05 vel fiance Cound to at least three decimal places 0 Ath 0.05 level, can it because that the men completion under en annements less than the scheduled mean?

Answer 1

Answer----->>

Here critical value calculate from t-distribution table.

enlivo We use pagen solutona given that An electomies manufacteering process has a scheduled meon complchon time of 5 minutes i.e. e=75 Jaum: under new management, the mean compliktion time u is less than 5 minuter nie. <75 Also given that Sample means 7 min Sample size ana 415 Sample standard deviation = 5= 9 min The bull bypothesis is Hoi u=75 The Altenattive hypothes is, H: WLAS Test Saliste Hence, samole size: 15 x 30 and 3 is unknown. t-test statistic Test statistical under Ho ta 7 70-75 -2.152 9/15 -211527 oftcal value at the d=0.05 -tant at Decision Rules Reject Ho if tt-tan- otherwise do not Reject Ho. Here, t = -2.152 k-toos 14 we reject to at 5% tevel of significance condusion Yes. At the o.os level it can be concluded that the mean completion time under new management is less than the scheduled mean. tooos, 14