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 0.12 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 0.019 is calculated.

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

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

Respuesta :

Answer:

The hypothesis to determine whether the vending machines are properly dispensing 12 ounces of coffee is:

H₀:  

Hₐ: Not all means are equal.

The ANOVA output is as follows:

One-way ANOVA: Machine A, Machine B, Machine C

Source           DF              SS                MS              F              P

Factor              2            8.363           4.182         31.73       0.000

Error               15             1.977            0.132

Total               17           10.340

The significance level is α = 0.05.

The p-value of the model is:

p-value = 0.000

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.000 < α = 0.05

The null hypothesis will be rejected.

Conclusion:

There is a significant difference between the means.

Step-by-step explanation:

Hope this helps:)