An automobile company is working on changes in a fuel injection system to improv

Question

An automobile company is working on changes in a fuel injection system to improve

gasoline mileage. A random sample of 15 test runs gives the following mileage (in miles per

gallon):

38 42 40 39 44 37 39 45

40 42 38 39 44 41 42

a) Find a two-sided 90% confidence interval for the mean gasoline mileage. State the

assumptions necessary to find the confidence interval.

b) The mean miles-per-gallon rating when using the previous fuel injection system was 35.

Can we conclude that new system has improved gasoline mileage? Use a level of

significance of 0.01.

Explanation / Answer

a)

Mean of the given dataset = sum of all observations / 15 = 10.67 = X

standard deviation of the sample = 2.36 = sd

mu = actual mean

Now, the confidence interval would be :

- t_14 <= (X - mu) / (sd / sqrt(n) ) <= t_14

where t is the student's T distribution with 14 degrees of freedom.

substituting,

- t_14 <= (40.67 - mu) / (2.36 / sqrt(15) ) <= t_14

from student T table we get t_14 as 1.761

substitute in the above equation and solve inequality on both sides to get the range of mu as :

39.54 <= mu <= 41.68

b)

Since 35 doesn't fall in the above confidence interval, we cannot conclude that new system has improved gasoline mileage.

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