Many drivers of cars that can run on regular gas actually buy premium in the bel

Question

Many drivers of cars that can run on regular gas actually buy premium in the belief that they will get better gas mileage. To test that belief, 12 cars in a company fleet were used. All the cars run on regular gas. Each car is filled first with either regular or premium gasoline, decided by a coin toss. The mileage for that tank of gas is recorded. Then the car is filled with the other type of gasoline and the mileage for that tank of gas is recorded. Below are the summary statistics for the difference in gas mileage between the two types of gasoline (premium - regular) for the 12 cars. mean = 3.2 miles per gallon SD 1.39 miles per gallon Is there evidence to indicate that gas mileage is higher when premium gas is used instead of regular gas, on average? a. Which of the following is the correct null hypothesis? B. Ho: diff-O where "diff"- miles per gallon for premium gas - miles per gallon for regular gas Oc. H prem ium regular where "premium" = miles per gallon using premium gas and "regular" = miles per gallon using regular gas b. Calculate the t-statistic. Round to two decimal places c. How many degrees of freedom does the t-statistic have?

Explanation / Answer

The statistical software output for this problem is:

One sample T summary hypothesis test:
: Mean of population
H0 : = 0
HA : > 0

Hypothesis test results:

Hence,

a) Option B is correct.

b) t = 7.97

c) Degrees of freedom = 11

Mean Sample Mean Std. Err. DF T-Stat P-value 3.2 0.40125844 11 7.9749102 <0.0001

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