Question

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with A random sample of 12 sample specimens has a mean compressive strength of psi. Round your answers to 1 decimal place. (a) Calculate the 95% two-sided confidence interval on the true mean compressive strength of concrete.

Answer 1

Complete Question

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with
`\sigma^2=1000`. A random sample of 12 sample specimens has a mean compressive strength of
`\=x=3207psi`. Round your answers to 1 decimal place. (a) Calculate the 95% two-sided confidence interval on the true mean compressive strength of concrete.

Answer:

`CI=(3189.1,3224.9)`

Explanation:

From the question we are told that:

Sample size
`n=12`

Standard deviation
`\sigma^2=1000psi^2\\\sigma=√(1000) \\\sigma=31.6`

Sample mean
`\=x=3207`

Confidence level =95%

`\alpha=100-95\\\alpha=0.05` significance level

From table \alpha 0.05

Gives

`Z_c=1.96`

Generally the equation for confidence interval is mathematically given by

`CI=(\=x-(z_c*\sigma)/(√(n) ) ),\=X+(Z_C*\sigma)/(√(12) ))`

`CI=(3207-(1.96*31.6)/(√(12) ) ),3207+(1.96*31.6)/(√(12) ))`

`CI=(3189.1,3224.9)`