Question 6.44

6.44 Fuel efficiency.

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 car was set to 60 miles per hour by cruise control, and the mpg were recorded at random times.13 Here are the mpg values from the experiment:

mileage

37.2 21.0 17.4 24.9 27.0 36.9 38.8 35.3 32.3 23.9
19.0 26.1 25.8 41.4 34.4 32.5 25.3 26.5 28.2 22.1

Suppose that the standard deviation of the population of mpg readings of this vehicle is known to be .

  1. What is , the standard deviation of ?
  2. Based on a 95% confidence level, what is the margin of error for the mean estimate?
  3. Given the margin of error computed in part (b), give a 95% confidence interval for , the mean highway mpg for this vehicle. The vehicle sticker information for the vehicle states a highway average of 27 mpg. Are the results of this experiment consistent with the vehicle sticker?