Question

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with σ = 31.62 psi. A random sample of 36 specimens has a mean compressive strength of 3250 psi. Suppose we wish to create a 99% confidence interval with a maximum width of 3 psi. What sample size is required?

Answer 1

Answer:

A sample size of at least 737 specimens is required.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.99}{2} = 0.005$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$.

So it is z with a pvalue of $1-0.005 = 0.995$, so $z = 2.575$

Now, find the width M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

$M = 3, \sigma = 31.62$

So:

$M = z*\frac{\sigma}{\sqrt{n}}$

$3 = 2.575*\frac{31.62}{\sqrt{n}}$

$3\sqrt{n} = 81.4215$

$\sqrt{n} = 27.1405$

$n = 736.60$

A sample size of at least 737 specimens is required.