Computers in some modern motorcycles calculate various quantities related to performance. One of these is fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one motorcycle equipped this way, the miles per gallon 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: 57.5 62.3 67.2 58.1 59.6 71.9 55.2 57.6 71.9 68.8 69.1 65.3 62.3 64.7 59.9 62.1 63.5 62.9 66.7 61.3

Part A Construct and interpret a 95% confidence interval for the mean fuel efficiency for this vehicle.

Part B A new motorcycle claims to have improved fuel efficiency over the previous model, getting a greater number of miles per gallon. An independent consumer agency takes a random sample of 30 records for fuel efficiency for this new model, and finds that the sample average is 65.9 mpg with a sample standard deviation of 3.2 mpg. Does this provide convincing evidence that the new model has greater fuel efficiency than the previous model? Explai

Part C Instead of the 95% confidence interval, the consumer agency decides to construct a 98% confidence interval for the mean fuel efficiency of the older model of motorcycle. What is this new confidence interval, and what does it mean in the context of this situation?

Part D Does your response to Part C change your conclusion in Part B? Why or why not? Be sure to specifically address the confidence level in your explanation.

Part E The consumer agency responsible for checking fuel efficiency claims wants to estimate the mean fuel efficiency for this new type of motorcycle within 0.5 mpg. How large a sample should be used? (8 points)