Does the concrete beat its 4000 psi target?

Question

A concrete supplier's mix is specified to cure at a mean compressive strength of 4000 psi. Historical testing fixes the standard deviation at $\sigma = 150$ psi. A batch of 36 cylinders averages 4035 psi.

Test at the 5% level (two-sided) whether the true mean strength differs from 4000 psi, and report the z-statistic.

Accepted Answer

With \sigma known, use a z-test. Hypotheses: H0: \mu = 4000 versus H1: \mu 
eq 4000. Standard error: 	ext{SE} = \frac{150}{\sqrt{36}} = \frac{150}{6} = 25 	ext{ psi}. Test statistic: z = \frac{4035 - 4000}{25} = \frac{35}{25} = 1.4. Since 1.4 = 1.4 < 1.96, we fail to reject H0. The two-sided p-value is 2\,[1 - \Phi(1.4)] = 2(0.0808) \approx 0.162, well above 0.05. Conclusion: the 35 psi surplus is within normal sampling noise; there is no significant evidence the mean differs from 4000 psi. Takeaway. "Fail to reject" does not mean the mean equals 4000 exactly, it means the data are consist…

Does the concrete beat its 4000 psi target?

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