Question

Conduct an appropriate hypothesis test using the provided information
[Neatly show all steps / necessary calculations, including both a complete comparison & interpretation statement AND plain English inference statement].

The National Center for Health Statistics reports that the mean total cholesterol level for all adults in the US last year was 203 with a population standard deviation of 36. In a sample of participants (n=3539) undergoing a dietary intervention clinical trial, the mean total cholesterol was 198. Using alpha = .05, is there a statistically significant difference between the study participants and the national average?

Answer 1

Solution:

The null and alternative hypothesis are

H₀: = 203 vs H_a: 203

Given

= 36

n = 3539

= 198

Use = 0.05

The test statistic z is given by

z =

= (198 - 203) / (36/3539)

= -8.26

Now , observe that ,there is   sign in H1. So , the test is two tailed.

p value = P(Z < -8.26) + P(Z > +8.26)

= 0 + 0

= 0.000

Since p value is less than = 0.05 , reject the null hypothesis

There is sufficient evidence to support that there a statistically significant difference between the study participants and the national average.