Question

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with σ² = 1000(psi)². A random sample of 12 specimens has a mean compressive strength ofx¯=3250psi

Construct a 95% two sided confidence interval on mean compressive strength.

Answer 1

confidence intervals (3232.10 , 3267.89)

Explanation:

Explanation:-

Confidence intervals on mean :-

The values χ ± 1.96 б/
`√(n)` is called the 95% of confidence intervals

Given sample size 'n' = 12

mean value 'x' = 3250

and variance σ² = 1000

now standard deviation σ =
`√(1000) = 31.622`

now the confidence interval ( χ - 1.96 б/
`√(n)` , χ + 1.96 б/
`√(n)` )

substitute given values and simplification , we get

`(3250 - 1.96(31.622)/(√(12) ) ,3250 +1.96(31.622)/(√(12) ))`

use calculator

95 % of confidence intervals are (3232.10 , (3267.89)

The given mean value is lies between in these confidence intervals

(3232.10 , (3267.89)