Type I and Type II errors
Managers at an automobile manufacturing plant would like to examine the mean completion time, mu, of an assembly line operation. The past data indicate that the mean completion time is 43 minutes, but the managers have reason to believe that this value has decreased. The managers plan to perform a statistical test.
After choosing a random sample of assembly line completion times, the managers compute the sample mean completion time to be 42 minutes. The standard deviation of the population of completion times can be assumed not to have changed from the previously reported value of 4 minutes.
Based on this information, answer the questions below.
What are the null hypothesis and the alternative hypothesis that should be used for the test? ________
In the context of this test, what is a type II error? _________
A type II error is__________, the null hypothesis that is µ is__________ when, in fact, µ is ________
Suppose that the managers decided not to reject the null hypothesis. What sort of error would they be making? ___________
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The solution provides the null and alternative hypothesis and interpretation of Type II error for a hypothesis testing problem.