Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

T 30. Gasoline Many drivers of cars that can run on regular gas actually buy pre

ID: 3052211 • Letter: T

Question

T 30. Gasoline 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, we use 10 cars from a company fleet in which all the cars run on regular gas. Each car is filled first with either regular or premium gasoline, decided by a coin toss, and the mileage for that tankful is recorded. Then the mileage is recorded again for the same cars for a tankful of the other kind of gaso- line. We don't let the drivers know about this experiment. Here are the results (miles per gallon): Car# 12345678910 Regular 16 20 21 22 23 22 27 25 27 28 Premium 19 22 24 24 25 25 26 26 28 32

Explanation / Answer

a.

Paired T-Test and CI: Regular, Premium

Paired T for Regular - Premium

N Mean StDev SE Mean
Regular 10 23.1000 3.7253 1.1780
Premium 10 25.1000 3.4464 1.0899
Difference 10 -2.00000 1.41421 0.44721


95% lower bound for mean difference: -2.81979
T-Test of mean difference = 0 (vs > 0): T-Value = -4.47 P-Value = 0.999


Paired T-Test and CI: Previous year, Current year

Paired T for Previous year - Current year

N Mean StDev SE Mean
Previous year 11 453.455 137.446 41.442
Current year 11 475.818 154.633 46.624
Difference 11 -22.3636 40.6258 12.2491

mean of difference = Dbar = -2

sd of difference = sdD = 1.414

The following null and alternative hypotheses need to be tested:

Ho: D >=0

Ha: D < 0

t= Dbar / [ sdD/sqrt(n) ] = -4.472

The p-value is p = 0.0008.

p value < alpha = 0.05

it is concluded that the null hypothesis is rejected.

b. The 90% confidence interval is -2.82 <D<1.18.

Regular premium difference 16 19 -3 20 22 -2 21 24 -3 22 24 -2 23 25 -2 22 25 -3 27 26 1 25 26 -1 27 28 -1 28 32 -4