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# Difference Amount Types of Gasoline

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Martin Motors has in stock three cars of the same make and model. The president would like to compare the gas consumption of the three cars (labeled car A, car B, and car C using four different types of gasoline. For each trial, a gallon of gasoline was added to an empty tank, and the car was driven until it ran out of gas.

The following table shows the number of miles driven in each trial.

Distance (miles)
Types of Gasoline Car A Car B Car C
Regular 22.4 20.8 21.5
Super regular 17.0 19.4 20.7
Unleaded 19.2 20.2 21.2

Using the .05 level of significance:
a. Is there a difference amount types of gasoline?
b. Is there a difference in the cars?

A regional commuter airline selected a random sample of 25 flights and found that the correlation between the number of passengers and the total weight, in pounds, of luggage stored in the luggage compartment is 0.94.
Using the .05 significance level, can we conclude that there is a positive association between the two variables?

A suburban hotel derives its gross income from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.
Using the .05 significance level, can we conclude that there is a positive association between the two variables?

Day Income Occupied Day Income Occupied
1 \$1,452 23 14 \$1,425 27
2 1,361 47 15 1,445 34
3 1,426 21 16 1,439 15
4 1,470 39 17 1,348 19
5 1,456 37 18 1,450 38
6 1,430 29 19 1,431 44
7 1,354 23 20 1,446 47
8 1,442 44 21 1,485 43
9 1,394 45 22 1,405 38
10 1,459 16 23 1,461 51
11 1,399 30 24 1,490 61
12 1,458 42 25 1,426 39
13 1,537 54

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#### Solution Summary

The difference in the amount types of gasoline with 0.05 level of significance is determined for Martin Motors.

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## Experimenting with Different Octane Gases

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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