Question: [18 marks] The level of calcium in the blood in healthy young adults varies with mean about 9.5 mg/dL and standard deviation about σ = 0.4. A clinic in rural Guatemala measures the blood calcium level of 180 healthy pregnant women at their first visit for prenatal care. The mean is \(\bar{X}\) = 9.58.

Is this an indication that the mean calcium level in the population from which these women come differs from 9.5? To answer this question, follow the following steps:

1. [2 marks] State Hp and Ha.
2. [12 marks] Carry out the test and give the p-value, assuming that σ = 0.4 in this population. Report your conclusion.
3. [4 marks] Give a 95% CI for the mean calcium level µ in this population.

Note: From your result in part (c), you are confident that µ lies quite close to 9.5. This illustrates the fact that a test based on a large sample (n=180 here) will often declare even a small deviation from Ho to be statistically significant.

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