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 eleven metropolitan areas across the upper Midwest region (OhioGasPrices.com website, March 18, 2012) Click on the datafile logo to reference the data. DATA file 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 Shell BP Marathon 3.77 3.72 3.87 3.76 3.83 3.85 3.93 3.79 3.78 3.81 3.69 3.83 3.83 3.85 3.77 3.84 3.84 4.04 3.78 3.84 3.84 3.83 3.78 3.87 3.89 3.79 3,87 3.87 3.99 3.79 3.79 3.86 3.86 Use α .05 to test for any significant difference in the mean price of gasoline for the three brands. Round SS to 6 decimals, MS to 6 decimals, F to 2 decimals and p to 3 decimals, if necessary. If your answer is zero, enter "O". Source DF MI Metropolitan Area 0.01073 о 10 Error 20 Total 0.14995 The p-value is Select your answer

Answer 1

Given information is related to the price per gallon for regular gasoline Let the brands be Shell, BP, Marathon. The objective is to test the significance difference in the mean price of gasoline for the three brands The objective of the problem is analyzed by suing Two-way Anova Setup the null and alternative hypothesis та Null hypothesis: There is no significant difference in the mean price of gasoline for the three brands Alternative hypothesis There is a significant difference in the mean price of gasoline for the three brands Let the level of significance be, α-0.05 Input the given data as follows in the Minitab C2-T C3 Metropolitan AreaBrand Response 3.77 1 Akron, OH 2 Cincinnati, OH Shell Shell 3 Cleveland, OH 4 Columbus, OH S Ft. Wayne, IN 6 Idianapolis, IN 7 Lansing, M 8 Lexington, KY 9 Louisville. KY 10 Muncie, iN 11 Toledo, OH 12 Akron, OH 13 Cincinnati, OH 14 Cleveland, OH 15 Columbus, OH 16 Ft. Wayne,IN 17 Idianapolis, IN 18 Lansing. MI 19 Lexington,KY 20 Louisville, KY 21 Muncie, IN 22 Toledo, OH 23 Akron, OH 24 Cincinnati, OH 25 Cleveland, OH 26 Columbus, OH 27 Ft. Wayne, IN 28 Idianapolis, IN 29 Lansing. M 30 Lexington, KY 31 Louisville. KY 32 Muncie, IN 33 Toledo, OH 3.76 3.83 Shell 3.79 3.70 Shell 3.83 3.83 3.85 3.03 Marathon 3.79 3.87 3.99 3.79 3.79 Marathon Marathon

Steps involved in the construction of two-way ANOVA using MINITAB are as below: Step 1: export the given data to MINITAB worksheet Step 2: Go to Stat Step 3: Select ANOVA option from the stat option. Step 4: click on Balanced ANOVA Step 5: Double click on Response to shift it into Responses Step 6: Input Metropolitan Area in the response box. Step 7: Input Brand to shift it into Model Step 8: Click ok. The following output is obtained as follows ANOVA: Response versus Metropolitan Area, Brand Factor Information Factor Levels Values Area Fixed 11 Akron, OH, Cincinnati, OH, Cleveland, OH, Columbus, OH, Ft Wayne, IN, Idianapolis, IN, Lansing. MI Lexington, KY Louisville, KY, Muncie, IN, Toledo, OH Brand Fixed 3 BP, Marathon, Shell Analysis of Variance for Response Source DF MS Metropolitan Area 10 0.10801 0.010801 8.30 0.000 Brand 2 0.01584 0.007918 6.08 0.009 20 0.02603 0.001302 32 0.14987 Error Total Model Summary R-sq(ad 0.0360765 82.6396 72.2196 The two-way ANOVA table is, Source of Variation d.f SS MSFp-value Metropolitan Area10 0.1080 0.0108 8.300.000 Brand Error Total 20.0158 0.0079 6.08 0.009 20 0.0260 32 0.1499 From the above anova table Since, the P-value 0.009 is less than the significance level 0.05, Therefore, there is an enough evidence to reject the null hypothesis Hence, there is a sufficient evidence to conclude that there is a significant difference in the mean price of gasoline for the three brands