The level of calcium in the blood of healthy young adults fo

The level of calcium in the blood of healthy young adults follows a Normal distribution with mean p = 10 milligrams per deciliter and standard deviation o = 0.4. A clinic measures the blood calcium of 100 healthy pregnant young women at their first visit for prenatal care. The mean of these loo measurements is = 9.8. Is this evidence that the mean calcium level in the population of healthy pregnant young women is less than 10? To answer this, test the hypotheses H0 : p = 10 versus H : p

Solution

(a) The test statistic is

Z=(xbar-mu)/(s/vn)

=(9.8-10)/(0.4/sqrt(100))

=-5

It is a left-tailed test.

So the p-value= P(Z<-5) =0 (from standard normal table)

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(b) Since the p-value is less than 0.05, we reject Ho.

Answer: Ho should be rejected