Question

The level of calcium in the blood of healthy young adults follows a normal distribution with mean μ = 10 milligrams per deciliter and standard deviation σ = 1.2. 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 bar = 9.8.  Is this evidence that the mean calcium level in the population from which these women come is less than 10?  To answer this, test the hypotheses H0: µ = 10, Ha: µ < 10 at the 5% significance level.

a. what is the value of the test statistic, z?

b. what is the p-value for this test?

Answer 1

Given

mean= μ = 10 milligrams per deciliter

standard deviation= σ = 1.2

Sample size = n = 100

sample mean = = 9.8

significance level = = 0.05

Hypotheses

H₀: µ = 10

H_a: µ < 10

Test statistic :

From standard normal table, the probability ( area) corresponding to the z-score of -1.67 is 0.0475

The P-Value is .0475

Since the P-value (0.0475) is less than the significance level (0.05) , reject the null hypothesis.