In: Statistics and Probability
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.