91.2k views
2 votes
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 ( , ).

User Kimmie
by
7.3k points

1 Answer

2 votes

Answer:

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

User Jclangst
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.