Question

In order to determine the average commute of college students, a researcher gathers data from a group of 50 students at the local college. This sample yieldied a mean of 14 and a standard deviation of 1.9.

Required:
Construct a 90% confidence interval for the population mean from the provided data.

Answer 1

13.5579875<x<14.44201244

Explanation:

The formula for calculating the confidence interval is expressed as:

CI = x+/- z × s/\sqrt{n}

x us the mean = 14

Z is the 90% CI = 1.645

S is the standard deviation = 1.9

n is the sample size = 50

Substitute.

CI = 14+/-1.645×1.9/7.07106.

CI = 14+/-1.645×0.26870057

CI = (14-0.44201244, 14+0.44201244)

CI = 13.5579875, 14.44201244

Hence the required interval is 13.5579875<x<14.44201244