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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
The alternate hypothesis is
since the value is less than this is a one tailed test.
Z=x bar-x/d/
where x is sample mean and d is standard deviation.
Z=15.4-15.5/1.7/
=-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.