8. An automotive engineer wanted to determine whether the octane of gasoline use

Question

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 23.8 27.1 26.4 26.1 28.4 25.3 89 Octane 28.4 26.9 26.1 26.4 28.9 25.1 92 Octane 28.7 27.2 26.8 27.3 29.1 25.8 Chev Impala r 300M Ford Taurus Lincoln LS Toyota Cam Volvo 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 ource DE Facto 1 918.68 918.68 1905.36 0.000 Error 34 Total 35 5006.46 7.77 2.58 S" 1.607 R-Sq 98.25% R-Sq(adj) 98.20% - " Two-way ANOVA: MPG versus Brand of Car, Octane DF MS Source Brand of Car 5 18.5911 3.71822 3.22 0.054 Octane Srror Total 2 5.1411 2.57056 2.23 0.158 10 11.5389 1.1539 7 35.2711 1.074 R-Sa 67.293 R-Sa(ad44.38 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.

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: 1 = 2 = 3

Alternative hypothesis: At-least one of the is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F = 2.23

The P-value = 0.158

Interpret results. Since the P-value (0.158) is greater than the significance level (0.05), we have to accept the null hypothesis.

Conclusion:-

Retain the H0, There is not sufficient evidence for significant differences between the three octane levels.

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