Question: Calcium level in pregnant women in rural Guatemala. The level of calcium in the blood in healthy young adults varies with mean about $9.5$ milligrams per deciliter and standard deviation about \(\sigma=0.4\). A clinic in rural Guatemala measures the blood calcium level of 160 healthy pregnant women at their first visit for prenatal care. The mean is \(\bar{x}=9.57 .\) Is this an indication that the mean calcium level in the population from which these women come differs from 9.5?

1. State \(H_{0}\) and \(H_{a}\).
2. Carry out the test and give the \(P\) -value, assuming that \(\sigma=0.4\) in this population. Report your conclusion.
3. Give a \(95 \%\) confidence interval for the mean calcium level \(\mu\) in this population. We are confident that \(\mu\) lies quite close to 9.5. This illustrates the fact that a test based on a large sample \((n=160\) here $)$ will often declare even a small deviation from \(H_{0}\) to be statistically significant.

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