Pt 6

8. An automotive engineer wanted to determine whether the octane of gasoline used in a car increases gas mileage. He selected six different brands of car and assigned a driver to each car. The miles per gallon was calculated for each car at each level of octane: 87 Octane 89 Octane 92 Octane Chev Impala 23.8 28.4 28.7 Chrysler 300M 27.1 26.9 27.2 Ford Taurus 26.4 26.1 26.8 Lincoln LS 26.1 26.4 27.3 Toyota Camry 28.4 28.9 29.1 Volvo 25.3 25.1 25.8 An assistant was in charge of the analysis of this data and was unsure whether one-way or two-way ANOVA should be used, so he performed both. The output is provided below, and you are to use the correct output to answer the questions. One-way ANOVA: MPG, Brand of Car Source DF SS MS F Factor 1 4918 . 68 4918 . 68 1905. 36 0.000 Error 34 87. 77 2 . 58 Total 35 5006 . 46 S = 1. 607 R-Sq = 98.25% R-Sq (adj) = 98.208 Two-way ANOVA: MPG versus Brand of Car, Octane Source DF SS MS F P Brand of Car 5 18 . 5911 3 . 71822 3.22 0 . 054 Octane 2 5 . 1411 2 . 57056 2 . 23 0 . 158 Error 10 11 . 5389 1. 15389 Total 17 35. 2711 S = 1.074 R-Sq = 67.298 R-Sq (adj ) = 44.38% Is there sufficient evidence at alpha=0.05, that the mean miles per gallon is different among the three octane levels? Remember to show all parts of the hypothesis test you use and use the computer output given (null and alternative, p-value, decision, interpretation)