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

A sample size of at least 737 specimens is required.

Explanation:

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

`\alpha = (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*(\sigma)/(√(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*(\sigma)/(√(n))`

`3 = 2.575*(31.62)/(√(n))`

`3√(n) = 81.4215`

`√(n) = 27.1405`

`n = 736.60`

A sample size of at least 737 specimens is required.