A. A. You have just been hired by the EPA to help with the new gas mileage stand

Question

A. A. You have just been hired by the EPA to help with the new gas mileage standards on new automobiles. The EPA would like to post average gas mileage as a 88% confidence interval. Suppose you collect data on 51 new Honda Accords and the average gas mileage for this sample was 29 with a sample standard deviation of 4.1. What is the HIGHER endpoint of your confidence interval? Be sure to use 2 decimal places.

B. After doing your Honda Accord study, you now have to go out and find the average gas mileage for the new Honda Pilot. If you want a 90% confidence interval with a maximum margin of error of 2.1, what sample size is necessary? Use a presample standard deviation of 6.3. Remember, no decimal this time. Round up!

Explanation / Answer

A) here std error of mean =std deviation/(n)1/2 =4.1/(51)1/2 =0.574

for 88% CI and (n-1=50) degree of freedom critical value of t =1.5818

therefore HIGHER endpoint of your confidence interval =sample mean + t*std error =29 +1.5818*0.574=29.91

B)

here for 90% CI ;z =1.6445

for margin of error E =2.1

hence required sample size n=(z*std deviation/E)2 =~ 25

please revert for any clariificaiton.

( Note : in part A t distriution is used even sample size is greater then 30 cause we do not know anything about population distribution and population std deviation is not known)

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