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 2.53 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.

Answer 1

The 90% confidence interval is
`2.47<\mu < 2.59`

Explanation:

From the question we are told that

The sample size is n = 6

The sample mean is
`\= x = 2.53 \ mm`

The standard deviation is
`\sigma  =  0.090\ mm`

Given that the confidence level is 90% then the level of significance is

`\alpha =  (100 - 90)\%`

=>
`\alpha =  0.10`

Generally from the normal distribution table the critical value of
`(\alpha )/(2)` is

`Z_{(\alpha )/(2) } =  1.645`

Generally the margin of error is mathematically represented as

`E =1.645 *  (0.090 )/(√(6) )`

=>
`E = 0.060`

Generally 90% confidence interval is mathematically represented as

`\= x -E <  \mu <  \=x  +E`

`2.53  -0.060 <\mu < 2.53  + 0.060`

=>
`2.47<\mu < 2.59`