Question

6. It is known that the mean cholesterol level for all Americans is 190. Construct the relevant hypothesis test to show that only children have an average higher cholesterol level than the national average. We test 100 only children and find out the mean is 198. You can use your own confidence level. (All Americans Standard Deviation is 15)

Answer 1

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: Children do not have an average higher cholesterol level than the national average.

Alternative hypothesis: Ha: Children have an average higher cholesterol level than the national average.

H0: µ = 190 versus Ha: µ > 190

This is an upper or right tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 190

Xbar = 198

σ = 15

n = 100

α = 0.05

Critical value = 1.6449

(by using z-table or excel)

Z = (198 - 190)/[15/sqrt(100)]

Z = 5.3333

P-value = 0.0000

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that children have an average higher cholesterol level than the national average.