Question

Wenton Powersports produces dune buggies. They have three assembly lines, “Razor,” “Blazer,” and “Tracer,” named after the particular dune buggy models produced on those lines. Each assembly line was originally designed using the same target production rate. However, over the years, various changes have been made to the lines. Accordingly, management wishes to determine whether the assembly lines are still operating at the same average hourly production rate. Production data (in dune buggies/hour) for the last eight hours are as follows. (You may find it useful to reference the F table.)

Razor				Blazer				Tracer
	11				10				9
	10				8				9
	8				11				11
	10				9				8
	9				11				8
	9				10				7
	13				11				8
	11				8				9

a. Specify the competing hypotheses to test whether there are some differences in the mean production rates across the three assembly lines.

• H₀: μ_Razor = μ_Blazer = μ_Tracer. H_A: Not all population means are equal.

• H₀: μ_Razor ≤ μ_Blazer ≤ μ_Tracer. H_A: Not all population means are equal.

• H₀: μ_Razor ≥ μ_Blazer ≥ μ_Tracer. H_A: Not all population means are equal.

b-1. Construct an ANOVA table. Assume production rates are normally distributed. (Round intermediate calculations to at least 4 decimal places. Round "SS" to 2 decimal places, "MS", "p-value" to 4 decimal places, and "F" to 3 decimal places.)

b-2. At the 5% significance level, what is the conclusion to the test?

Do/Do not reject HO, we can/cannot conclude that the mean/buggies hour differ for some production lines.

b-3. What about the 10% significance level?

Answer 1

a) The null and the alternative hypothesis is:

H₀: μ_Razor = μ_Blazer = μ_Tracer. H_A: Not all population means are equal.

b-1)

The ANOVA is done in excel.

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	8	81	10.1250	2.4107
Column 2	8	78	9.7500	1.6429
Column 3	8	69	8.6250	1.4107
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	9.75	2	4.8750	2.6765	0.0922	3.4668
Within Groups	38.25	21	1.8214
Total	48	23

b-2) Since p value > 0.05, so at 5% level of significance we do not reject H₀.

we cannot conclude that the mean/buggies hour differ for some production lines.

b-3) If level = 0.1, then p-value <0.1. In that case we reject H₀.

we can conclude that the mean/buggies hour differ for some production lines.