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
	12				10				9
	11				8				9
	9				11				10
	10				9				9
	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.)

ANOVA
Source of Variation		SS	df	MS	F	p-value	F crit
Between Groups
Within Groups
Total

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

(Reject, 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?

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

Answer 1

Given :

Production data (in dune buggies/hour) for the last eight hours are as follows.

Razor		Blazer		Tracer
	12				10				9
	11				8				9
	9				11				10
	10				9				9
	9				11				8
	9				10				7
	13				11				8
	11				8				9

a) Hypothesis test :

The null and alternative hypothesis is

H₀: μ_Razor = μ_Blazer = μ_Tracer.

H_A: Not all population means are equal.

b-1) Data summary :

Using software

Groups	N	Mean	Std.Dev	Std error
1	8	10.5	1.5119	0.5345
2	8	9.75	1.2817	0.4532
3	8	8.625	0.9161	0.3239

ANOVA table :

Source	df	SS	MS	F	P-VALUE
Between groups	k-1= 3-1 =2	14.25	SSB/df1 = 7.1250	SSB/SSW = 4.483	0.0239
Within Groups	N-k = 24-3 = 21	33.37	SSW/df2 = 1.5893
Total	23	47.62

b-2) Since P-value is less than significance level 0.05, we reject the null hypothesis.

Conclusion : At 5% significance level, reject Ho. We can conclude that the mean buggies/hour differ for some production lines.

b-3) Since P-value is less than significance level 0.10, we reject the null hypothesis.

Conclusion : At 10% significance level, reject Ho. We can conclude that the mean buggies/hour differ for some production lines.