A particular article presents a study of the effect of the s

A particular article presents a study of the effect of the subbase thickness on the amount of surface deflection caused by aircraft landing on an airport runway. In six applications of a 160 kN load on a runway with a subbase thickness of 862 mm, the average surface deflection was 2.09 mm with a standard deviation of 0.080 mm. Find a90% confidence interval for the mean deflection caused by a 160 kN load. When necessary round intermediate and final calculations to three decimal places. The confidence interval is

Solution

The degree of freedom =n-1=6-1=5

Given a=1-0.9=0.1, t(0.05, df=5) =2.02 (from student t table)

So the lower bound is

xbar - t*s/vn = 2.09 -2.02*0.08/sqrt(6) = 2.024

So the upper bound is

xbar + t*s/vn = 2.09 +2.02*0.08/sqrt(6) =2.156