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	50	41
	Intermediate	54	44
	Full-sized	64	47

Use α = 0.05 to test for any significant differences.

State the null and alternative hypotheses.

H₀: μ_Computerized = μ_Electronic
H_a: μ_Computerized ≠ μ_ElectronicH₀: 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-sizedH₀: μ_Computerized ≠ μ_Electronic
H_a: μ_Computerized = μ_ElectronicH₀: μ_Compact ≠ μ_Intermediate ≠ μ_Full-sized
H_a: μ_Compact = μ_Intermediate = μ_Full-sized

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

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

p-value =

State your conclusion.

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.     Do not 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.

Answer 1

(a)

Correct option:

(b)

From the given data, the following statistics are calculated:

n1 = 3

1= 56

s1 = 7.2111

n2 = 3

2 =44

s2 = 3.00

Test statistic is:

t = (56 - 44)/4.5093

= 2.66

ndf = n1+ n2 - 2

=4

By Technology, P - Value = 0.1170

(c)

Correct option:

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