Question

You may need to use the appropriate technology to answer this question.

The price drivers pay for gasoline often varies a great deal across regions throughout the United States. The following data show the price per gallon for regular gasoline for a random sample of gasoline service stations for three major brands of gasoline (Shell, BP, and Marathon) located in 11 metropolitan areas across the upper Midwest region.†

Metropolitan Area	Shell	BP	Marathon
Akron, Ohio	3.77	3.83	3.78
Cincinnati, Ohio	3.72	3.83	3.87
Cleveland, Ohio	3.87	3.85	3.89
Columbus, Ohio	3.76	3.77	3.79
Ft. Wayne, Indiana	3.83	3.84	3.87
Indianapolis, Indiana	3.85	3.84	3.87
Lansing, Michigan	3.93	4.04	3.99
Lexington, Kentucky	3.79	3.78	3.79
Louisville, Kentucky	3.78	3.84	3.79
Muncie, Indiana	3.81	3.84	3.83
Toledo, Ohio	3.69	3.83	3.86

Use α = 0.05 to test for any significant difference in the mean price of gasoline for the three brands.

State the null and alternative hypotheses.

H₀: μ_Shell = μ_BP = μ_Marathon
H_a: μ_Shell ≠ μ_BP ≠ μ_MarathonH₀: Not all the population means are equal.
H_a: μ_Shell = μ_BP = μ_Marathon    H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.H₀: μ_Shell ≠ μ_BP ≠ μ_Marathon
H_a: μ_Shell = μ_BP = μ_MarathonH₀: μ_Shell = μ_BP = μ_Marathon
H_a: Not all the population means are equal.

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 there is a significant difference in the mean price per gallon for regular gasoline among the three brands.

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference in the mean price per gallon for regular gasoline among the three brands.    

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference in the mean price per gallon for regular gasoline among the three brands.

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference in the mean price per gallon for regular gasoline among the three brands.

Answer 1

Solution:

State the null and alternative hypotheses.

Answer:

Not all the population means are equal.

We can use the excel ANOVA data analysis tool to find the answers to the given question. The excel output is given below:

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

Answer:

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

Answer:

State your conclusion.

Answer: Reject H₀. There is sufficient evidence to conclude that there is a significant difference in the mean price per gallon for regular gasoline among the three brands.