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 = 10 milligrams per deciliter and standard deviation = 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 100 measurements is x = 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 : = 10 versus Ha : < 10 at the 5% significance level.

(a) What is the value of the P-value?
(b) Determine which of the following statements is true.

• H0 should be rejected.
• H0 should not be rejected.
• Ha should be rejected.
• There is a 5% chance that the null hypothesis is true.

Solution

To test the hypotheses H₀ : = 10 versus Ha : < 10 at the 5% significance level.

we calculate test statistics as sigma value is know it will follow normal distribution

Cal z = (xbar - ) / ( /sqrt(n))

xbar = 9.8, = 0.4, = 10, n = 100

Cal z = -5

P- value using R software is < 0.00001

b) Statement: H0 should be rejected as p-value < 0.00001 which is < 0.05 therefore we do not have enough evidence to accept H0