Bootstrap distribution of the mpg standard deviation. Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the mpg were recorded each time the gas tank was filled, and the computer was then reset. Here are the mpg values for a random sample of 20 of these records:
In addition to the average mpg, the driver is also interested in how much variability there is in the mpg.
(a) Calculate the sample standard deviation s for these mpg values.
(b) We have no formula for the standard error of s. Find the bootstrap standard error for s. Use 1000 resamples.
(c) What does the standard error indicate about how accurate the sample standard deviation is as an estimate of the population standard deviation?
(d) Would it be appropriate to give a bootstrap t interval for the population standard deviation? Why or why not?