Given the information in Exercise 11.76, and using the 0.01 level of significance in comparing the sample standard deviations, were we justified in assuming that the population standard deviations were equal? Would your conclusion change if the standard deviation of the data values with the rooftop carrier had been 0.07 gallons?
In exercise 11.76
The manufacturer of a small utility trailer is interested in comparing the amount of fuel used in towing the trailer with that required to overcome the weight and wind resistance of a rooftop carrier. Over a standard test route at highway speeds, 8 trips with the trailer resulted in an average fuel consumption of 0.28 gallons, with a standard deviation of 0.03. Under similar conditions, 10 trips with the rooftop carrier led to an average consumption of 0.35 gallons, with a standard deviation of 0.05 gallons.