Question

From a national perspective, it was reported that students living off-campus took an average of 32.0 minutes to travel to school. A recent study of 25 randomly chosen students living off-campus here at Humber College took an average of 34.5 minutes with a standard deviation of 3.0 minutes.

a.    With this sample data and the assumption that the distribution of travel times follow a normal distribution, develop the 98% confidence interval for the average time it takes for students here at Humber College to travel to school. (3)

b.    By examining this confidence interval, does it seem reasonable that the students here at Humber College take longer or less time or about the same time to travel to school as the national average? Explain. (1,1)

Answer 1

(a)

SE = s/

= 3.0/

= 0.6

= 0.02

ndf = n - 1 = 25 - 1 = 24

From Table, critical values of t = 2.4922

Confidence Interval:

34.5 (2.4922 X 0.6)

= 34.5 1.4953

= ( 33.0047 ,35.9953)

Confidence Interval:

33.0047 < < 35.9953

(b)

Since all values of the Confidence Interval are greater than 32, we conclude that it seems reasonable that the students here at Humber College take longer time to travel to school as the national average