Managers at an automobile manufacturing plant would like to examine the mean completion time,μ, of an assembly line operation. The past data indicate that the mean completion time is 41 minutes, but the managers have reason to believe that this value has increased. 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 43 minutes. The standard deviation of the population of completion times can be assumed not to have changed from the previously reported value of 6minutes. Based on this information, answer the questions below. What are the null hypothesis (H0) and the alternative hypothesis ( H1) that should be used for the test? H0 :μ is ? less than ? less than or equal to ? greater than? greater than or equal to? not equal to? equal to ? 6 ? 43 ? 41? H1 :μ is ? less than ? less than or equal to? greater than? greater than or equal to? not equal to? equal to ?6 ? 43? 41? In the context of this test, what is a Type I error? A Type I error is ?rejectingfailing to reject the hypothesis that μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?64341 when, in fact, μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?64341. Suppose that the managers decide not to reject the null hypothesis. What sort of error might they be making? ?Type IType II

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Description: Managers at an automobile manufacturing plant would like to examine the mean completion time,μ, of an assembly line operation. The past data indicate that the mean completion time is 41 minutes, but the managers have reason to believe that this value

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Managers at an automobile manufacturing plant would like to examine the mean completion time,μ, of an assembly line operation. The past data indicate that the mean completion time is 41 minutes, but the managers have reason to believe that this value has increased. 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

43 minutes. The standard deviation of the population of completion times can be assumed not to have changed from the previously reported value of

6minutes.

Based on this information, answer the questions below.

What are the null hypothesis (H0) and the alternative hypothesis ( H1) that should be used for the test?

H0 :μ is ? less than ? less than or equal to ? greater than? greater than or equal to? not equal to? equal to ? 6 ? 43 ? 41?

H1 :μ is ? less than ? less than or equal to? greater than? greater than or equal to? not equal to? equal to ?6 ? 43? 41?

In the context of this test, what is a Type I error?

A Type I error is ?rejectingfailing to reject the hypothesis that

is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?64341 when, in fact,

is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?64341.

Suppose that the managers decide not to reject the null hypothesis. What sort of error might they be making? ?Type IType II

Expert Solution

Step 1

The hypothesis can be formed as

$H_{0} : μ = 41 H_{A} : μ > 41$

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