Question

The compressive strength of concrete is being tested by a civil engineer who tests 12 specimens and finds that the sample mean is 3259.9 psi and the sample standard deviation is 35.57 psi. Compressive strength is known to be normally distributed.
Find a 95% confidence interval for mean compressive strength.

Answer 1

Answer:

The 95% confidence interval for mean compressive strength is:

$3237.3\leq \mu\leq 3282.5$

Step-by-step explanation:

We have a sample of n=12 specimens, with sample mean=3259.9 and sample standard deviation = 35.57.

We know the population is normally distributed.

For a 95% confidence interval and df=n-1=11, the t-statistic is t=2.201.

Then, the CI can be expressed as:

$M-t*s/\sqrt{N}\leq \mu\leq M+t*s/\sqrt{N}\\\\3259.9-2.201*35.57/\sqrt{12}\leq \mu\leq 3259.9+2.201*35.57/\sqrt{12}\\\\ 3259.9-22.6\leq \mu\leq 3259.9+22.6\\\\3237.3\leq \mu\leq 3282.5$