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. 25 21 26 6 25 14 26 24 7 10 14 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

Solution

Let X = commute (miles) that non-residential students have to their college

Let mean and standard deviation of X be μ and σ.,

Back-up Theory

100(1 - α) % Confidence Interval for population mean μ, when σ is not known is: Xbar ± MoE

where

MoE = (t_{n- 1, α /2})s/√n

with

Xbar = sample mean,

t_{n – 1, α /2} = upper (α/2)% point of t-distribution with (n - 1) degrees of freedom,

s = sample standard deviation and

n = sample size.

Now, to work out the solution,

Part (a)

To compute the confidence interval distribution to be used is t-distribution since population standard deviation is not known. Answer 1

Part (b)

90% confidence interval for the population mean commute for non-residential college students is between 1

3. 66 and 22.34 miles. Answer 2

Details of calculations follow at the end.

Part (c)

If many groups of 11 randomly selected non-residential college students are surveyed, then 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. Answer 3

Details of calculations

n	11
Xbar	18.0000
s	7.949843
√n	3.316625
α	0.1
n - 1	10
tα/2	1.812461
(s/√n)(tα/2)	4.344411
Lower Bound	13.65559
Upper Bound	22.34441

DONE