Consider the following scenario: Bill works at a factory and monitors the produc

Question

Consider the following scenario:

Bill works at a factory and monitors the production output of one of the machines. He conducts an ANOVA test to test the hypothesis that the mean output of the machine is not affected by which operator is using the machine. There are three different operators who use the machine on different days of the week, and Bill records the output of the machine on a series of randomly selected days for each of the three operators. A one-way ANOVA test is conducted with a level of significance of 0.05. A P-value of 0.13 is calculated.

Barbara also monitors the production output of this machine. In a completely independent test to Bill, Barbara tries to determine if the mean output of the machine is affected by the quality of the raw materials that are used with the machine. Barbara develops three categories of quality: Good, Average, and Poor. For each quality grade, Barbara randomly selects a series of days when that quality grade of material is used with the machine. She records the output of the machine on each day. A one-way ANOVA test is conducted with a level of significance of 0.05. A P-value of 0.015 is calculated.

Select the correct statement in relation to the above two ANOVA tests and the use of the Bonferroni method:

Neither Bill nor Barbara will find use in the Bonferroni method. Barbara may find use in the Bonferroni method, but Bill will not. Both Bill and Barbara may find use in the Bonferroni method. Bill may find use in the Bonferroni method, but Barbara will not.

Explanation / Answer

The correct option is D

Barbara may find use in the Bonferroni method, but Bill will not.

Explanation:

The Bonferroni method is an example of a multiple-comparisons method. It is a method that is used if an ANOVA test is conducted and the null hypothesis is rejected. Specifically, the Bonferroni method is used when it is determined that not all of the means being tested in an ANOVA test are equal. The method is used to determine which pairs of means differ from one another. In his ANOVA test, Bill tests the following hypotheses:

H0: The mean output of the machine is not affected by the machine operator

Ha: The mean output of the machine is affected by the machine operator

Bill uses a level of significance of 0.05. A P-value of 0.13 is calculated. Therefore Bill does not reject the null hypotheses, and so he retains the hypothesis that the mean output of the machine is not affected by the machine operator. Therefore Bill has no use for the Bonferroni method, since he is not in a position to ask which pairs of machine operators differ (because the result of his test is that he retains the hypothesis that they don't differ). In her ANOVA test, Barbara tests the following hypotheses:

H0: The mean output of the machine is not affected by the quality of raw material

Ha: The mean output of the machine is affected by the quality of raw material

Barbara uses a level of significance of 0.05. A P-value of 0.018 is calculated. Therefore Barbara rejects the null hypothesis, and concludes that the mean output of the machine is affected by the quality of the raw materials used.

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