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 14 randomly selected non-residential college students. Round answers to 3 decimal places where possible.

10

21

26

20

18

12

11

16

17

6

14

25

25

6

a. To compute the confidence interval use a ? z t  distribution.

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

c. If many groups of 14 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

(a) To compute the confidence interval, we use a t distribution with 13 (= n - 1) degrees of freedom, since the population standard deviation is unknown to us.
(c) If many groups of 14 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. 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.
(b) With 90% confidence the population mean commute for non-residential college students is between 13.030 and 19.398 miles (working is given below).