Question

For each scenario below, do the following:

1. (1) Indicate which procedure you would use: (i) two-independent sample t-test, (ii) paired t- test, (iii) chi-square goodness-of-fit test, (iv) chi-square test of independence, (v) t-test of a regression coefficient, (vi) an F −test for multiple regression, (vii) a one-way ANOVA, or (viii) a two-way ANOVA.
2. (2) Based on your answer in (1), state the appropriate null and alternative hypotheses.
3. (3) For all procedures except (i), state the degrees of freedom(s) for the corresponding test statistic.

(d) Does premium octane gasoline improve gas mileage? Suppose an experiment is conducted to test the claim that cars running on premium gas get better gas mileage than the same car running on regular gas. In the experiment, 10 cars are used (all cars are the same make and model). For each car, a coin is tossed. If heads comes up, then the car: first drives on 12 gallons of regular gas, the mileage driven is measured, then the car drives on 12 gallons of premium gas, after which the mileage driven is measured. If the coin comes up tails, the same procedure is used, except premium gas is used first. The experiment is blinded in that the drivers are not told the type of gas in the car.

Answer 1

d)

1)

I would use paired t test.

Because for same car we measure mileage, one for regular car, another for premium gas.

2)

Let we find mileage difference between then. Xd= mileage for normal gas - mileage for premium gas.

Xd follows a distribution with mean d.

H0: d= 0, mileage is same for both normal and premium gas.

Ha: d < 0, mileage for premium gas is more than normal gas.

3) degrees of freedom =10-1=9

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