Question

The table below contains the overall miles per gallon​ (MPG) of a type of vehicle.

28

29

24

22

29

32

23

25

35

32

35

23

26

34

Choose the correct answer below.

A.We have 95​% confidence that the mean MPG of this type of vehicle for the sample is contained in the interval.

B. 95​% of the sample data fall between the limits of the confidence interval.

C. The mean MPG of this type of vehicle for 95​% of all samples of the same size is contained in the interval.

D. We have 95​% confidence that the population mean MPG of this type of vehicle is contained in the interval.

Answer 1

sample mean, xbar = 28.3571
sample standard deviation, s = 4.651
sample size, n = 14
degrees of freedom, df = n - 1 = 13

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.16

ME = tc * s/sqrt(n)
ME = 2.16 * 4.651/sqrt(14)
ME = 2.685

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (28.3571 - 2.16 * 4.651/sqrt(14) , 28.3571 + 2.16 * 4.651/sqrt(14))
CI = (25.67 , 31.04)

D. We have 95​% confidence that the population mean MPG of this type of vehicle is contained in the interval.