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.

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

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

a) To test whether there are some differences in the mean production rates across the three assembly lines, i.e.

H₀: μRazor = μBlazer = μTracer. H_A: Not all population means are equal.

b-1) The ANOVA table is mentioned in the image.

b-2) Since P-value = 0.113 > 0.05,so at 5% level of significance we fail to reject the null hypothesis and we can conclude that all population means are almost equal.

b-3) Since P-value = 0.113 > 0.10,so at 10% level of significance we fail to reject the null hypothesis and we can conclude that all population means are almost equal.