##### Question

In: Statistics and Probability

# Data on the fuel economy of several 2010 model vehicles are given in the accompanying table....

Data on the fuel economy of several 2010 model vehicles are given in the accompanying table. Complete parts​ (a) and​ (b) below.

 Car mpg 1 29 2 35 3 35 4 28 5 38 6 32 7 22 8 27 9 31 10 32 11 28 12 36 13 24 14 25 15 27

​a) Find and interpret a​ 95% confidence interval for the gas mileage of 2010 vehicles. Select the correct choice below and fill in the answer boxes within your choice.

​(Round to two decimal places as needed. Use ascending​ order.)

A.One is​ 95% confident that the true mean gas mileage for cars like the ones in the sample is between __ mpg and ___mpg.

B.The true mean gas mileage for cars like the ones in the sample is between ___mpg and ___mpg​ 95% of the time.

C.​95% of all cars like the ones in the sample have gas mileages between ___mpg and ___ mpg

D.One is​ 95% confident that the gas mileage of a randomly selected car like the ones in the sample is between ___ mpg and ___ mpg

​b) Does this confidence interval capture the mean gas mileage for all 2010​ vehicles? Choose the correct answer below.

A.There is a​ 95% chance that this interval contains the true mean gas mileage for all 2010 vehicles.

B.Because the sample size is more than​ 10% of the​ population, the inferences drawn from the confidence interval are not valid.

C.Without knowing how the data were​ selected, one must be cautious about generalizing to all 2010 cars.

D.Assuming the population of 2010 gas mileages follows a Normal​ model, this confidence interval definitely captures the true mean.

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