Question

(Use Excel or R)

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.

Razor				Blazer				Tracer
	11				10				9
	10				8				9
	8				11				10
	10				9				9
	9				9				8
	9				10				7
	13				13				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 "Sum Sq" to 2 decimal places, "Mean Sq" and "F value" to 3, and "p-value" to 4 decimal places.)

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

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

Answer 1

Using Excel: Data > Data Analysis > Anova: Single Factor

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Razor	8	81	10.125	2.410714
Blazer	8	78	9.75	2.785714
Tracer	8	69	8.625	0.839286
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit at 0.05
Between Groups	9.75	2	4.875	2.423	0.113017	3.4668
Within Groups	42.25	21	2.012
Total	52	23

a. Null and Alternative hypothesis:

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

b-1. ANOVA table.

Source of Variation	SS	df	MS	F	P-value
Between Groups	9.75	2	4.875	2.423	0.1130
Within Groups	42.25	21	2.012
Total	52	23

b-2. As p-value = 0.01130 > 0.05, we fail to reject the null hypothesis.

There is not enough evidence to conclude that not all population means are equal.

b-3. As p-value = 0.01130 > 0.10, we fail to reject the null hypothesis.

There is not enough evidence to conclude that not all population means are equal.