In a test of Premium Gasoline, a random sample of 35 people used the premium gas

Question

In a test of Premium Gasoline, a random sample of 35 people used the premium gasoline. After a year, their mean mileage improvement was 2.5 miles with a standard deviation of 4.2 miles. Assume mileage improvement is normally distributed.

(a) What conditions are needed to construct a 95% confidence interval estimate of the mean mileage improvement for all the subjects? Are these conditions met?

(b) Construct a 95% confidence interval estimate of the mean mileage improvement

(c) Interpret the interval found in part b

(d) Does the premium gasoline appear to be effectieve?

Explanation / Answer

(a) Following are the conditions needed to construct a confidence interval :

Since the sample of 35 people is random, this condition is satisfied.

Since we considering the same 35 people for improvement in gasoline mileage, the data is paired.

We are given that mileage improvement is normally distributed. Hence, this condition is also satisfied.

(b) (1-alpha)% confidence interval estimate of the mean mileage improvement wil be :

Lower limit : Xd - t(n-1,alpha/2) * ( Sd / ?n )

Upper limit : Xd + t(n-1,alpha/2) * ( Sd / ?n )

We are given,

Xd = 2.5

Sd = 4.2

n = 35

alpha = 0.05

t(n-1,alpha/2) = t(35-1 , 0.05/2) =t(34 , 0.025) = 2.345

Lower limit : 2.5 - 2.345 * (4.2 / ?35 ) = 0.8352

Upper limit : 2.5 + 2.345 * (4.2 / ?35 ) = 3.3352

95% confidence interval estimate of the mean mileage improvement is : ( 0.8352 , 3.3352 )

(c) If repeated samples were taken and the 95% confidence interval computed for each sample, 95% of the intervals like the above interval would contain the population mean mileage improvement.

Basically the interval ( 0.8352 , 3.3352 ) is a range of values that you can be 95% certain contains the true mean mileage improvement of the population.

(d) We can see that the interval ( 0.8352 , 3.3352 ) does not contain 0, which means that mean mileage improvement can never be 0. Hence, we can that the premium gasoline appear to be effective.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.