. Binomial c. Student t d. F Many drivers of cars that can run on regular gas ac
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Question
. Binomial c. Student t d. F Many drivers of cars that can run on regular gas actually buy premium gas in the belief that they will get better gas mileage. To test that belief, a consumer research group evaluated the use of 10 cars in a company fleet in which all the cars run on regular gas. Each car was filled first with either regular or premium gas, decided by a coin toss, and the mileage for that tankful was recorded. Then the mileage was recorded again for the same cars for a tankful of the other kind of gas miles per gallon) are shown in the worksheet "Gas Data" foun significance, is there evidence that cars get better gas mileage on average with premium gas? Include all six steps of the hypothesis test. The results (in d on Isidore. Using a 0,05 level ofExplanation / Answer
Here we have to test that,
H0 : Mud = 0 Vs H1 : Mud < 0
where Mud is population mean difference between regular and premium.
Assume alpha= level of significance = 0.05
Here we use paired t test.
The test statistic follows t-distribution.
t = dbar / (Sd/ sqrt(n))
where dbar = mean difference between the points.
n is number of data pairs
Sd is the standard deviation of the difference between the points
We can do Paired t test in MINITAB.
steps :
ENTER data into MINITAB sheet --> Stat --> Basic statistics --> Paired t --> Samples in columns --> First sample : select regular --> Second sample : select Premium --> Options --> Confidence level : 95.0 --> Test mean : 0.0 --> Alternative : less than --> ok --> ok
Welcome to Minitab, press F1 for help.
Paired T-Test and CI: regular, premium
Paired T for regular - premium
N Mean StDev SE Mean
regular 10 23.10 3.73 1.18
premium 10 25.10 3.45 1.09
Difference 10 -2.000 1.414 0.447
95% upper bound for mean difference: -1.180
T-Test of mean difference = 0 (vs < 0): T-Value = -4.47 P-Value = 0.001
Test statistic = -4.47
P-value = 0.001
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : There is sufficient evidence to say that the cars get significantly better fuel economy with fuel gas.
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