# ANOVA

Case Study - The Higher the Better?

Max knew that gas companies advertise the higher octane of gas result in higher gas mileage? He wanted to know if the higher price would be offset by the higher amount of miles per gallon. So, he found some friends who would help him with an experiment.

He asked 9 of his buddies (total of 10 for the experiment) who drove cars if they would help him find out. Max told everyone to keep track of their mileage for the next three times they filled their tanks with gas. The first time they filled their tank they must use Regular Unleaded 87 octane gas, on the second time, Mid-grade Unleaded 89 octane gas, and on the last fill-up they would use the expensive Super-Unleaded 92 octane gas. At each fill-up Max instructed his buddies to calculate the miles per gallon they had received from each of the different octane of gas.

When the experiment was over, Max collected the miles per gallon information from each of his nine buddies and recorded the data in a table like the one below.

1. What is the hypothesis that Max is investigating?

2. What is the independent variable?

What are the levels of the independent variable?

3. What is the dependent variable?

4. Which statistical test would he use to test his hypothesis?

5. For each of the sets of output below, what can you tell about the dependent variable? What decision would the student make?

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Case Study - The Higher the Better?

Max knew that gas companies advertise the higher octane of gas result in higher gas mileage? He wanted to know if the higher price would be offset by the higher amount of miles per gallon. So, he found some friends who would help him with an experiment.

He asked 9 of his buddies (total of 10 for the experiment) who drove cars if they would help him find out. Max told everyone to keep track of their mileage for the next three times they filled their tanks with gas. The first time they filled their tank they must use Regular Unleaded 87 octane gas, on the second time, Mid-grade Unleaded 89 octane gas, and on the last fill-up they would use the expensive Super-Unleaded 92 octane gas. At each fill-up Max instructed his buddies to calculate the miles per gallon they had received from each of the different octane of gas.

When the experiment was over, Max collected the miles per gallon information from each of his nine buddies and recorded the data in a table like the one below. ...

#### Solution Summary

The expert examines experimenting with different octane gases. Step by step method for computing test statistic for One way ANOVA is given in the answer.