Laurel Springs School
AP STATIST
AP STATIST 101
Question
Answered step-by-step
Computers in some modern motorcycles calculate various quantities...
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
...[Show More]
Laurel Springs School
AP STATIST
AP STATIST 101
Question
Answered step-by-step
Computers in some modern motorcycles calculate various quantities...
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. (8 points)
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?
Explain. (8 points)
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? (8 points)
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. (8 points)
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)
Please write the work in text. Thank you :)
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