Conduct Analysis of Variance on the Randomized Complete Block Design $\mu _ { 1 }$

Short Answer

Conduct Analysis of Variance on the Randomized Complete Block Design
-A researcher wants to determine whether the type of gasoline used in a car affects the gas mileage. Gas mileage is also affected by car type and driver. The researcher selects five different types of car and assigns a driver to each car. For each car (and driver), the researcher randomly selects the sequence in which the different gasoline types will be used. The mileage for each car/gasoline combination was determined by filling the car with 3 gallons of the specified gasoline, driving the car around a race track until the gas tank was empty, and dividing the number of miles driven by the number of gallons used. The results are shown in the table. The mileages are given in miles per gallon. Let $\mu _ { 1 }$ be the mean for gasoline $A , \mu _ { 2 }$ the mean for gasoline $B$ , and $\mu _ { 3 }$ the mean for gasoline $\mathrm { C }$ . In a test of $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ versus $\mathrm { H } _ { 1 }$ : at least one of the means is different, the null hypothesis is rejected at the $\alpha = 0.05$ level of significance. Use Tukey's test to determine which pairwise means differ using a familywise error rate of $\alpha = 0.05$ . Give the $\mathrm { P }$ -value for each of the pairwise tests and state your conclusion.
$\begin{array}{l|c|c|c} & \text { Gasoline A } & \text { Gasoline B } & \text { Gasoline C } \\\hline \text { Car 1 } & 25.1 & 24.6 & 26.9 \\\text { Car 2 } & 26.3 & 26.2 & 27.1 \\\text { Car 3 } & 24.3 & 24.0 & 25.8 \\\text { Car 4 } & 28.1 & 27.4 & 28.5 \\\text { Car 5 } & 27.7 & 27.8 & 28.6\end{array}$