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The Case of the Different Gasoline Types
A young, cost-conscious college student was concerned that he wasn’t getting the best value
for his gasoline dollar. After all, didn’t the gasoline companies advertise that the higher grades of
gasoline would lead to higher gas mileage? The student knew that the higher grades cost more but
wondered if the higher cost would be offset by the higher number of miles per gallon. Always willing to
save a buck, the student decided to run an experiment.
The student found nine friends, all of whom owned cars, that were willing to be a part of the
experiment. The student explained that the ten of them (including himself) would keep track of the next
three times they filled up their gas tanks. On the first fill-up, they would all use Regular gasoline, on the
second they would use Super gasoline and on the third they would use Ultra gasoline. At each fill-up
the student conducting the research instructed his friends to compute the miles per gallon they had
gotten from each of the brands of gas.
At the end of the study, the student researcher collected the miles per gallon information from
each student and plotted it into a table like the one seen below. Now, all he had to do was figure out
how to appropriately analyze the data!
Car 1 2 3 4 5 6 7 8 9 10
Regular 22 15 14 25 12 15 15 9 15 12
Super 22 15 14 25 12 15 15 9 15 15
Ultra 24 17 12 22 14 11 16 11 14 9
1. What is the hypothesis that the student 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?
Case A:
Gas Type N Mean Standard Standard
Deviation Error of
the Mean
Regular 10 15.4 4.7422 1.4996
Super 10 15.7 4.5959 1.4533
Ultra 10 15.00 4.8762 1.5420
All Brands 30 15.37 4.5825 .8366
Sum of Degrees of Mean F value p value
Squares Freedom Square
MPG Between 2.467 2 1.233 .055 .947
Groups
Within 606.500 27 22.463
Groups
Total 608.967 29
Comparison Mean Difference Standard Error p value
Regular to Super .30 2.120 .990
Regular to Ultra .40 2.120 .982
Super to Ultra .70 2.120 .947
Case B:
Gas Type N Mean Standard Standard
Deviation Error of
the Mean
Regular 10 20.40 4.4771 1.4158
Super 10 15.70 4.5959 1.4533
Ultra 10 15.00 4.8762 1.5420
All Brands 30 17.03 5.1090 .9328
Sum of Degrees of Mean F value p value
Squares Freedom Square
MPG Between 172.467 2 86.233 3.983 .030
Groups
Within 584.500 27 21.648
Groups
Total 756.967 29
Comparison Mean Difference Standard Error p value
Regular to Super 4.7 2.081 .097
Regular to Ultra 5.4 2.081 .049
Super to Ultra .70 2.081 .945
Case C:
Gas Type N Mean Standard Standard
Deviation Error of
the Mean
Regular 10 20.4 4.4771 1.4158
Super 10 15.7 4.5959 1.4533
Ultra 10 45.0 6.2716 1.9833
All Brands 30 27.03 13.9913 2.5545
Sum of Degrees of Mean F value p value
Squares Freedom Square
MPG Between 4952.47 2 2476.2 92.282 .000
Groups
Within 724.500 27 26.833
Groups
Total 5676.97 29
Comparison Mean Difference Standard Error p value
Regular to Super 4.7 2.317 .147
Regular to Ultra 24.6 2.317 .000
Super to Ultra 29.3 2.317 .000

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1) The xxxxxxx that the xxxxxxx is investigating xxxxxxx xxxxxxx the xxxxxxx grades of xxxxxxx leads to xxxxxxx gas xxxxxxx xxxxxxx advertised by xxxxxxx gasoline companies.

2) xxxxxxx variable is xxxxxxx type of xxxxxxx gasoline used. xxxxxxx of gasoline xxxxxxx xxxxxxx Super xxxxxxx Ultra

3) Dependant xxxxxxx is the xxxxxxx per xxxxxxx xxxxxxx student can xxxxxxx “sum of xxxxxxx to test xxxxxxx hypothesis.

5) For xxxxxxx A, 2-tailed xxxxxxx is equal xxxxxxx xxxxxxx therefore xxxxxxx is a xxxxxxx difference in xxxxxxx two xxxxxxx xxxxxxx sum of xxxxxxx and p-value xxxxxxx positive, therefore xxxxxxx is a xxxxxxx in the xxxxxxx per gallon xxxxxxx xxxxxxx the xxxxxxx will reject xxxxxxx gasoline companies’ xxxxxxx 2-tailed xxxxxxx xxxxxxx Regular to xxxxxxx is .990>.5.

The xxxxxxx p-value for xxxxxxx to Ultra xxxxxxx .982>.5.

The 2-tailed xxxxxxx for Super xxxxxxx xxxxxxx is xxxxxxx the student xxxxxxx use the xxxxxxx brand xxxxxxx xxxxxxx case B, xxxxxxx p-value is xxxxxxx to .030<.05, xxxxxxx there is xxxxxxx significant difference xxxxxxx the two xxxxxxx xxxxxxx is xxxxxxx increase in xxxxxxx mileage per xxxxxxx (MPG).  xxxxxxx xxxxxxx student will xxxxxxx the gasoline xxxxxxx advertisement.

The 2-tailed xxxxxxx for Regular xxxxxxx Super is xxxxxxx 2-tailed p-value xxxxxxx xxxxxxx to xxxxxxx is .049<.5.

The xxxxxxx p-value for xxxxxxx to xxxxxxx xxxxxxx .945>.5.

Hence the xxxxxxx will use xxxxxxx Ultra brand xxxxxxx gas.

For case xxxxxxx 2-tailed p-value xxxxxxx equal to xxxxxxx xxxxxxx there xxxxxxx no difference xxxxxxx the two xxxxxxx There xxxxxxx xxxxxxx increase in xxxxxxx mileage per xxxxxxx (MPG).  Hence xxxxxxx student will xxxxxxx the gasoline xxxxxxx advertisement.

The 2-tailed xxxxxxx xxxxxxx Regular xxxxxxx Super is xxxxxxx 2-tailed p-value xxxxxxx Regular xxxxxxx xxxxxxx is .000<.5.

The xxxxxxx p-value for xxxxxxx to Ultra xxxxxxx .000<.5.

Hence the xxxxxxx will use xxxxxxx Super brand xxxxxxx xxxxxxx

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