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:

$CI=(3189.1,3224.9)$

Step-by-step explanation:

From the question we are told that:

Sample size $n=12$

Standard deviation $\sigma^2=1000psi^2\\\sigma=\sqrt{1000} \\\sigma=31.6$

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

$CI=(\=x-\frac{z_c*\sigma}{\sqrt{n} } ),\=X+\frac{Z_C*\sigma}{\sqrt{12} })$

$CI=(3207-\frac{1.96*31.6}{\sqrt{12} } ),3207+\frac{1.96*31.6}{\sqrt{12} })$

$CI=(3189.1,3224.9)$