Question

An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow.

		Analyzer
		Computerized	Electronic
Car	Compact	51	42
	Intermediate	55	43
	Full-sized	62	47

Use α = 0.05 to test for any significant differences.

A) State the null and alternative hypotheses.

H₀: μ_Computerized = μ_Electronic = μ_Compact = μ_Intermediate = μ_Full-sized
H_a: Not all the population means are equal.

H₀: μ_Compact = μ_Intermediate = μ_Full-sized
H_a: μ_Compact ≠ μ_Intermediate ≠ μ_Full-sized    

H₀: μ_Computerized = μ_Electronic
H_a: μ_Computerized ≠ μ_Electronic

H₀: μ_Compact ≠ μ_Intermediate ≠ μ_Full-sized
H_a: μ_Compact = μ_Intermediate = μ_Full-sized

H₀: μ_Computerized ≠ μ_Electronic
H_a: μ_Computerized = μ_Electronic

B) Find the value of the test statistic. (Round your answer to two decimal places.) ____

C) Find the p-value. (Round your answer to three decimal places.)

p-value = ____

D) State your conclusion.

Reject H₀. There is sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers.

Reject H₀. There is not sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers.    

Do not reject H₀. There is sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers.

Do not reject H₀. There is not sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers.

Answer 1

The statistical software output for this problem is:

Hence,

a) Hypotheses:

H0: μCompact = μIntermediate = μFull-sized
Ha: μCompact ≠ μIntermediate ≠ μFull-sized

b) Test statistic = 0.09

c) p - Value = 0.958

d) Do not reject H0. There is not sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers. Option D is correct.