Question

An 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 864 mm, the average surface deflection was 2.34 mm with a standard deviation of 0.090 mm. Find a 90% confidence interval for the mean deflection caused by a 160 kN load. Round the answers to three decimal places. The 90% confidence interval is ( , ).

Answer 1

The answer is below

Explanation:

The z score is used to determine by how many standard deviations the raw score is above or below the mean.

Given that: sample size (n) = 6, standard deviation (σ) = 0.09 mm, mean (μ) = 2.34 mm

The confidence interval = 90% = 0.9

α = 1 - 0.9 = 0.1

α / 2 = 0.05

The z score of 0.05 is the same as the z score of 0.45 (0.5 - 0.05) which is 1.645.

The margin of error is given as:

`E=Z_{(\alpha)/(s) }*(\sigma)/(√(n) )`

`E=1.645*(0.09)/(√(6) )=0.06\ mm`

The confidence interval = μ ± E = 2.34 ± 0.06 = (2.28, 2.40)

The confidence interval is between 2.28 mm and 2.4 mm