Question

You are interested in finding a 90% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 11 randomly selected non-residential college students. Round answers to 3 decimal places where possible.

23

8

9

7

7

16

7

14

6

24

17

a. To compute the confidence interval use a

distribution.

b. With 90% confidence the population mean commute for non-residential college students is between and miles.

c. If many groups of 11 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of commute miles and about percent will not contain the true population mean number of commute miles.

Answer 1

sample mean, xbar = 12.545
sample standard deviation, s = 6.6538
sample size, n = 11
degrees of freedom, df = n - 1 = 10

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.812

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (12.545 - 1.812 * 6.6538/sqrt(11) , 12.545 + 1.812 * 6.6538/sqrt(11))
CI = (8.91 , 16.18)

About 90 percent of these confidence intervals will contain the true population mean number of commute miles and about 10 percent will not contain the true population mean number of commute miles.