Question

A customer wants to know whether the mean chest compression resulting from an institute crash test is the same for family​ cars, passenger​ vans, and trucks. The data to the right were collected from the​ institute's study.

	Vehicle Type	Chest Compression left parenthesis mm right parenthesisChest Compression (mm)
	Family CarsFamily Cars	36	42	39	37	31	44
	Passenger VansPassenger Vans	30	31	33	26	30	34
	TrucksTrucks	34	28	36	37	35	28

a. Conduct a​ one-way ANOVA test on the data.

b. Interpret your results from​ (a) at the 11​% significance level.

c. Decide whether presuming that the assumptions of normal populations and equal population standard deviations are met is reasonable.

Part 1) Conduct a​ one-way ANOVA test on the data. What is the​ F-statistic?

F = ?

Part 2) Determine the critical value of Fa

Fa = ?

Part 3) State the Conclusion

Since the F-static _ in the rejection region, _ H0. The data _ sufficient evidence to conclude that the population means are not all the same.

Answer 1

a. Conduct a​ one-way ANOVA test on the data.

	Mean	n	Std. Dev
	38.2	6	4.62	Family CarsFamily Cars
	30.7	6	2.80	Passenger VansPassenger Vans
	33.0	6	4.00	TrucksTrucks
	33.9	18	4.87	Total
ANOVA table
Source	SS	df	MS	F	p-value	F critical
Treatment	176.78	2	88.389	5.86	.0131	2.57
Error	226.17	15	15.078
Total	402.94	17

b. Interpret your results from​ (a) at the 11​% significance level.

The results are significant.

c. Decide whether presuming that the assumptions of normal populations and equal population standard deviations are met is reasonable.

Part 1) Conduct a​ one-way ANOVA test on the data. What is the​ F-statistic?

F = 5.86

Part 2) Determine the critical value of Fa

Fa = 2.57

Part 3) State the Conclusion

Since the F-static is in the rejection region, reject H0. The data provides sufficient evidence to conclude that the population means are not all the same.

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