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 σ = 0.4. A clinic in rural Guatemala measures the blood calcium level of 160 healthy pregnant women at their ?rst visit for prenatal care. The mean is x = 9.57. Is this an indication that the mean calcium level in the population from which these women come differs from 9.5?

(a) State H0 and Ha.

(b) Carry out the test and give the P-value, assuming that σ = 0.4 in this population. Report your conclusion.

(c) Give a 95% con?dence interval for the mean calcium level μ in this population. We are con?dent that μlies 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 H0 to be statistically signi?cant.