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Paul [167]
3 years ago
5

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is approximately normally distributed w

ith 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.
Engineering
1 answer:
prohojiy [21]3 years ago
3 0

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

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