Question

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is approximately normally distributed with variance σ2 = 800 psi2. It is desired to estimate the compressive strength with an error that is less than 13 psi at 95% confidence. What sample size is required? Round your answer up to the nearest whole number. The answer must be exact.

Answer 1

Answer:

19

Explanation:

The minimum sample size is given by

$p(|x\bar-\mu|$

$-\frac {E}{\frac {\sigma}{\sqrt n}} \leq -z_{\alpha/2}$ hence making n the subject

$n \geq (\frac {z_{\alpha/2}\times \sigma}{E})^{2}$

Standard deviation, $\sigma=\sqrt variance$ hence $\sigma=\sqrt 800$

Significance level, $\alpha$=1-Confidence=1-0.95=0.05

Critical value=$z_{\apha/2}=z_{0.025}$ and from z table the critical value is 1.96

$n \geq (\frac {z_{\alpha/2}\times \sigma}{E})^{2}=(\frac {1.96\times \sqrt 800}{13})^{2}= 18.18509\approx 19$

The minimum n has to be an integer hence we round it off to the nearest whole number