Question

Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of minutes. The standard deviation of completion times was minutes. An analyst at the company suspects that, under new management, the mean completion time, , is now less than minutes. To test this claim, a random sample of completion times under new management was taken by the analyst. The sample had a mean of minutes. Assume that the population is normally distributed. Can we support, at the level of significance, the claim that the population mean completion time under new management is less than minutes

Answer 1

No, we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.

Given mean of 15.5 minutes , standard deviation of 1.7 minutes, sample size of 90 and sample mean of 15.4 minutes.

We can do the following study for conclusion:

Firstly the null hypothesis is

$H_{0}: x=15.5$

The alternate hypothesis is

$H_{1}: x < 15.5$

since the value is less than this is a one tailed test.

Z=x bar-x/d/$\sqrt{n}$

where x is sample mean and d is standard deviation.

Z=15.4-15.5/1.7/$\sqrt{90}$

=-0.1/1.7/9.4868

=-0.560

Critical value of Z at 0.1 level of significance

Z=-1.28

We fails to reject the null hypothesis since -0.560>-1,28

Hence we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.

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Question is incomplete. It should include:

mean of 15.5 minutes ,

standard deviation of 1.7 minutes,

sample size of 90

and sample mean of 15.4 minutes.