Question

The level of magnesium in the blood of healthy young adults follows a normal distribution, with mean μ = 10 milligrams per deciliter and standard deviation σ = 0.4. A clinic measures the magnesium of 25 healthy pregnant young women at their first visit for prenatal care. The sample mean of these 25 measurements is 9.6. Is this evidence that the mean magnesium 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

The P-value of your test is

Question 4 options:

0.3085.

greater than 0.99.

0.6170.

less than 0.0002.

Answer 1

Solution :

The null and alternative hypotheses would be as follows:

Test statisic :

To test the hypothesis the most appropriate test would be one sample z-test for mean. The test statistic is given as follows:

Where, x̅ is sample mean, μ​​​​​ is hypothesized value of population mean under H​​0, σ is population standard deviation and n is sample size.

We have,  x̅ = 10, μ = 9.6, σ = 0.4 and n = 25

The value of the test statistic is -5.

P - value :

Since, our test is left-tailed test, therefore we shall obtain left-tailed p-value for the test statistic. The left-tailed p-value is given as follows :

p-value = P(Z < value of the test statistic)

p-value = P(Z < -5)

p-value = 0.0000

The p-value is 0.0000.

Hence, last option is correct which is as follows :

The p-value of the test is less than 0.0002.