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

Answer:

confidence intervals (3232.10 , 3267.89)

Step-by-step explanation:

Explanation:-

Confidence intervals on mean :-

The values χ ± 1.96 б/$\sqrt{n}$  is called the 95% of confidence intervals  

Given sample size 'n' = 12

mean value 'x' = 3250

and variance σ² = 1000

now standard deviation σ = $\sqrt{1000} = 31.622$

now the confidence interval ( χ - 1.96 б/$\sqrt{n}$ ,  χ + 1.96 б/$\sqrt{n}$ )

substitute given values and simplification , we get

$(3250 - 1.96\frac{31.622}{\sqrt{12} } ,3250 +1.96\frac{31.622}{\sqrt{12} })$

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)