Question

1.    In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Nine test vehicles of each type were crashed, with the results shown in the table below. Research question: Are the mean crash damages the same for these three vehicle types?

Crash Damage at 5 mph in Dollars ($)
Goliath	Varmint	Weasel
700	1700	2280
1400	1650	1670
850	1630	1740
1430	1850	2000
1740	1700	1510
1240	1650	2480
700	860	1650
1250	1550	1650
970	1250	1240

1. At the 0.05 level of significance, determine if there is a difference in the average crash damages by vehicle type. State your hypotheses and show all 7 steps clearly. (8 points)
2. Give and interpret the p-value. (3 points)
3. Should Tukey pairwise comparisons be conducted? Why or why not? (3 points)
4. If appropriate, use Minitab to produce Tukey pairwise comparison. Write a few sentences with your conclusions from those comparisons. (4 points)
5. Use Levene’s test to determine if the assumption of homogeneity of variances is valid. Give the hypotheses, test statistic, p-value, decision and conclusion. Use the 0.05 level of significance. (8 points)
6. Verify with Minitab by attaching or including relevant output (see parts a, d, and e). (6 points)

Answer 1

Treatments	Observations									Total
Goliath	700	1400	850	1430	1740	1240	700	1250	970	10280
Varmint	1700	1650	1630	1850	1700	1650	860	1550	1250	13840
Weasel	2280	1670	1740	2000	1510	2480	1650	1650	1240	16220
									Grand total	40340

Hypothesis

H₀:

H₁: Atleast one mean is different

ANOVA Table

Source of Variation	SS	df	MS	F	F crit
Between Groups	1985985	2	992992.6	8.062004	3.402826
Within Groups	2956067	24	123169.4
Total	4942052	26

From the ANOVA table we can see that calculated F-value is more than F-critical hence we reject null hypothesis and we conclude that there is significant difference between the treatments.

b) p-value = 0.002,since p-value is less than alpha hence we reject null hypothesis.

c) Since we concluded that there is significant difference between the treatments we have to perform Tukey's test to find which treatments differ.

d) minitab output for Tukeys test

Tukey Simultaneous Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
Varmint - Goliath	396	165	(-17, 809)	2.39	0.062
Weasel - Goliath	660	165	(247, 1073)	3.99	0.002
Weasel - Varmint	264	165	(-149, 677)	1.60	0.266

e) Levenes test

Tests

Method	Test Statistic	P-Value
Multiple comparisons	—	0.852
Levene	0.47	0.629

Since p-value ismore than 005 we fail to reject null hypothesis and conclude that all treatments have equal variances.

f) Minitab output

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	1985985	992993	8.06	0.002
Error	24	2956067	123169
Total	26	4942052