Question

You are interested in finding a 95% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 12 randomly selected non-residential college students. Round answers to 3 decimal places where possible.

5

15

25

16

17

26

6

6

11

5

8

19

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

b. With 95% confidence the population mean commute for non-residential college students is between  and   miles.

c. If many groups of 12 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

Answer)

As the population standard deviation is unknown, we will use t distribution to estimate the interval.

A)

t distribution

B)

First we need to find, mean and standard deviation of the given data

Mean = 13.25

S.d = 7.5814

Degrees of freedom is given by sample size - 1

Sample size is = 12

Degrees of freedom = 11

For degrees of freedom 11

And confidence level of 95%

Critical value t is = 2.201

Margin of error is = 2.201*(s.d/√n)

MOE = 4.8170242255830

Confidence interval is given by

(Mean - MOE, Mean + MOE)

(8.4329757744169, 18.067024225583)

(8.433, 18.067)

C)

About 95% of these confidence interval will contain the true population mean.