Question

An automotive parts supplier assesses the usability and quality of the door locks that they provide. The locks are manufactured at three different plants. The production manager wants to determine whether the plant affects the final product. The production manager collects data on locks from each plant, and gives a usability and quality rating. Data are found in the file Car Lock Ratings.

a) State the null and alternate hypothesis we would run to determine if the Usability rating across all three manufacturing plants is the same.

b) Run a one-way ANOVA on these data. Show output.

c) What conclusions can you make based on the p-value of this test?

d) Obtain boxplot, residuals scatter plot, and individual residual Normal probability plots.

e) Have all assumptions been met? Explain using your plots to illustrate your answer.

Usibility Rating
Plant A	Plant B	Plant C
5	6	5
6	4	4
5	5	6
6	4	6
6	3	5
5	4	7
4	5	6
3	5	5
4	6	4
5	5	4
4	5	4
3	6	5
6	7	5
7	7	6
8	6	5
6	7	6
8	6	6
7		5
6		6
5		7
6		5
7
7
8

Answer 1

(a) The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H_a: At least one means is not equal

(b) The One-Way ANOVA output is:

	Mean	n	Std. Dev
	5.7	24	1.46	Plant A
	5.4	17	1.17	Plant B
	5.3	21	0.91	Plant C
	5.5	62	1.21	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	1.98	2	0.988	0.67	.5174
Error	87.51	59	1.483
Total	89.48	61

(c) Since the p-value (0.5174) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we can conclude that the Usability rating across all three manufacturing plants is the same.

(d) The boxplot is:

The scatterplot is:

(d) The Normal Probability plots are:

(e) Yes, the assumptions are met.