T 30. Gasoline Many drivers of cars that can run on regular gas actually buy pre
ID: 3052186 • 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 2527 28 Premium 19 22 24 24 25 25 26 26 28 32Explanation / Answer
a.
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
From the sample data, it is found that the corresponding sample means are:
X1bar = 23.1 , X2bar= 25.1
Also, the provided sample standard deviations are:
s1 = 3.725, s2 = 3.446
and the sample size is n = 10. For the score differences we have
D bar -2, sD=1.414
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho: D 0
Ha: D > 0
This corresponds to a right-tailed test, for which a t-test for two paired samples be used.
T-Value = -4.47
The p-value is p = 0.9992 and since 0.9992 > 0.05, it is concluded that the null hypothesis is not rejected.
b. The 90% confidence interval is -2.82 < muD < -1.182.82<D<1.18.
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