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 seven applications of a 162 kN load on a runway with a subbase thickness of 868 mm, the average surface deflection was 2.08 mm with a standard deviation of 0.070 mm. Find a

90%

confidence interval for the mean deflection caused by a 162 kN load. Carry four significant digits throughout your calculations.

The confidence interval is (, ).

Solution

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=2.08
Standard deviation( sd )=0.07
Sample Size(n)=7
Confidence Interval = [ 2.08 ± Z a/2 ( 0.07/ Sqrt ( 7) ) ]
= [ 2.08 - 1.64 * (0.026) , 2.08 + 1.64 * (0.026) ]
= [ 2.037,2.123 ]