Question

13 Assignment 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 (OthioGasPrices.com website, March 18, 2012). Click on the datafile logo to reference the data. DATA file Shell Marathon 3.78 3.89 3.87 3.76 3.79 Metropolitan Area Akron, Ohio Cincinnati, Ohio Cleveland, Ohio Columbus, Ohio Ft Wayne, Indiana Indianapolis, Indiana Lansing, Michigan Lexington, Kentucky Louisville, Kentucky Muncie, Indiana Toledo, Ohio 3.93 3.87 3.99 3.79 3.78 3.81 ? 3.79 3.79 3.86 3.86 3.6 Use a = .05 to test for any significant difference in the mean price of gasoline for the three brands. If required, round your answers to four decimal places. If your answer is zero enter "0" Source of SS MS P-value F crit variation (to 4 decimals) of (to 4 decimals) (to 4 decimals) (to 4 decimals) (to 4 decimals) Rows Columns Error Total The p-value corresponding to Columns is What is your conclusion? - Select your answer -

Answer 1

Output using excel : Data > Data Analysis > Anova: Two-Factor Without Replication

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
Akron, Ohio	3	11.38	3.793333	0.001033
Cincinnati, Ohio	3	11.42	3.806667	0.006033
Cleveland, Ohio	3	11.61	3.87	0.0004
Columbus, Ohio	3	11.32	3.773333	0.000233
Ft. Wayne, Indiana	3	11.54	3.846667	0.000433
Indianapolis, Indiana	3	11.56	3.853333	0.000233
Lansing, Michigan	3	11.96	3.986667	0.003033
Lexington, Kentucky	3	11.36	3.786667	3.33E-05
Louisville, Kentucky	3	11.41	3.803333	0.001033
Muncie, Indiana	3	11.51	3.836667	0.000633
Toledo, Ohio	3	11.38	3.793333	0.008233
Shell	11	41.8	3.8	0.00468
BP	11	42.29	3.844545	0.004867
Marathon	11	42.36	3.850909	0.003829
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	0.1080	10	0.0108	8.3937	0.0000	2.3479
Columns	0.0169	2	0.0085	6.5764	0.0064	3.4928
Error	0.0257	20	0.0013
Total	0.1507	32

The p-value corresponding to Column is 0.0062

Conclusion:

Reject the null hypothesis. It is significant.