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Performing a one-tailed test

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An automobile assembly line operation has a scheduled mean completion time, mean, of 14.7 minutes. The standard deviation of completion times is 1.2 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 60 completion times under new management was taken. The sample had a mean of 14.6 minutes. Assume that the population is normally distributed.

Perform a one-tailed test.
null H0:
alternative H1:
This is a z test
The value of the test statistic is
The critical value at the 0.01 level of significance: (round to at least three decimal places)
Can we support the claim that the mean completion time has decreased under new management?

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Solution Summary

This solution contains a detailed explanation of how to perform a one-tailed test by the five-step procedure.

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An automobile assembly line operation has a scheduled mean completion time, mean, of 14.7 minutes. The standard deviation of completion times is 1.2 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 60 completion times under new management was taken. The sample had a mean of 14.6 ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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