An oil company has developed a new petroleum product designe

An oil company has developed a new petroleum product designed to improve the fuel efficiency of vehicles with petrol engines. In test the fuel efficiency of a random sample of 10 cars of the same make and model were driven at fixed speed on a gallon of the new fuel and the miles travelled recorded. The following figures were recorded:   37 38 40 35 36 35 39 37 40 37

The manufacturer of the car claims that the mean mileage per gallon for these vehicles (driven at the same speed as in these test) was 36. Test the hypothesis that the mean mileage per gallon is greater with the new fuel using the 1%leel of significance and comment on your results.

Solution

Set Up Hypothesis
Null, H0: U=36
Alternate,mean mileage per gallon is greater with the new fuel H1: U>36
Test Statistic
Population Mean(U)=36
Sample X(Mean)=37.4
Standard Deviation(S.D)=1.8379
Number (n)=10
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =37.4-36/(1.8379/Sqrt(10))
to =2.409
| to | =2.409
Critical Value
The Value of |t | with n-1 = 9 d.f is 2.821
We got |to| =2.409 & | t | =2.821
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 2.4088 ) = 0.01966
Hence Value of P0.01 < 0.01966,Here We Do not Reject Ho

we don\'t have evidence indicate that mean mileage per gallon is
greater with the new fuel