The owner of a large fleet of taxis is trying to estimate his costs for next yea

Question

The owner of a large fleet of taxis is trying to estimate his costs for next year's operations. Because of the high cost of gasoline, the owner has recently converted his taxis to operate on propane. In order to estimate what the average propane consumption will be he takes a random sample of 38 taxis and measures the miles per gallon achieved. The sample gave a mean of 34.26 miles per gallon with a variance of 29.61. If it can be assumed that the distribution of the mileages is normally distributed Find a 95% confidence interval estimate for the mean propane mileage of all taxis. Find a 90%i confidence interval estimate for the mean propane mileage of all taxis. Is it actually necessary that the distribution of mileages be normally distributed for the confidence intervals in (a) and (b) to be valid? Why or why not?

Explanation / Answer

a) 95% c.i=Xbar+-Z(s/sqrt N-1), where Xbar is sample mean, s is sample standard deviation and N i sample size, Z is critical Z score at alpha=0.05.

=34.26+-1.96(sqrt 29.61/sqrt 38-1)

=32.5066 to 36.0133

b) 90% ci=34.26+-1.65(sqrt 29.61/sqrt 38-1)

=32.7839 to 35.7360

c) The distribution of mileages be normally distributed for the confidence interval to be valid.

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