Question

A researcher wants to examine the production capability of three manufacturing plants that utilize different production methods of the same part in order to select a plant as a supplier for a company. The effectiveness of each plant will be measured in the number of parts it can produce in an hour. Representative hourly production amounts are recorded from each plant over a period of 12 hours and provided to the researcher.

The results of each of the three plants are as follows:

Plant A	Plant B	Plant C
131	141	108
111	165	185
165	174	190
188	185	206
175	172	175
173	188	197
188	145	186
186	177	221
145	162	214
132	151	211
128	147	214
123	133	208

1. Use the five-step hypothesis testing process and StatCrunch to evaluate this scenario. Perform a complete analysis and interpretation of the results. If appropriate, use diagrams or graphs. Ensure your answer is detailed in all aspects. Be sure to comment on the assumptions of the ANOVA and if there are any violations. Which manufacturing plant, if any, would you recommend as the supplier?  Why?  Write up your results in APA format.

Answer 1

The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: Not all means are not equal

	Mean	n	Std. Dev
	153.8	12	28.35	Plant A
	161.7	12	18.09	Plant B
	192.9	12	30.26	Plant C
	169.4	36	30.61	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	10,293.06	2	5,146.528	7.55	.0020
Error	22,507.83	33	682.056
Total	32,800.89	35

The p-value is 0.0020.

Since the p-value (0.0020) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a significant difference between the groups.

The graph is:

The assumptions of ANOVA are violated.

Plant C would be recommended as a supplier because it has the highest hourly production amounts.

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