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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