An electronics manufacturinf process has a scheduled mean completion time of 70

Question

An electronics manufacturinf process has a scheduled mean completion time of 70 minutes, It is claimed that, under new management, the mean completion time, is less than 70 minutes. To test this claim, a random sample of 13 completion times under new management was taken. The sample has a mean completion time of 66 minutes and a standad deviation of 10 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 mangement is less than the schedule mean? Perform a one-tailed test. State the null and alternative hypothesis, identify the cricial value, calculate the test statistic, state and explain your decision on the null hypothesis.

Explanation / Answer

The test hypothesis is
Ho:>=70
Ha:<70

The test statistic is

t=(xbar - )/(s/n)

=(66-70)/(10/sqrt(13))

=-1.44

Given a=0.05, the critical value is t(0.05, df=n-1=12)=-1.78 (check student t table)

Since t=-1.44>-1.78, we do not reject Ho.

So we can not conclude that under new mangement is less than the schedule mean.

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