90% interval for mean concrete strength

Question

A concrete supplier's compressive strength has a known population standard deviation of $\sigma = 250$ psi. A random sample of $n = 25$ cylinders has a mean strength of $\bar{x} = 4000$ psi.

Construct a 90% confidence interval for the true mean compressive strength.

Accepted Answer

Setup. With \sigma known, use \bar{x} \pm z^{}\,\sigma/\sqrt{n}. For 90% confidence, z^{} = 1.645. Compute. The standard error is \frac{250}{\sqrt{25}} = \frac{250}{5} = 50. Margin of error = 1.645 	imes 50 = 82.25, so 4000 \pm 82.25 = [3917.75,\ 4082.25]. Interpret. A 90% interval is narrower than a 95% one from the same data because 1.645 < 1.96. You trade coverage for a tighter estimate. Takeaway. Lower confidence levels give narrower intervals. Choose the level before looking at the data, based on how costly a miss is.

90% interval for mean concrete strength

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