Question

In a test of the effectiveness of garlic for lowering​ cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes​ (before minus​ after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 0.3 and a standard deviation of 2.11. Use a 0.01 significance level to test the claim that with garlic​ treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic​ treatment? Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

Answer 1

Let us denote the difference

d : choleterol levels before - choleterol levels after

To test against

Here

sample mean of difference

sample standard deviation of difference

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 1% level of significance if P-value < 0.01

Now,

The value of the test statistic

and P-value

Since P-value > 0.01, so we fail to reject H₀ at 1% level of significance and we can conclude that the mean change in LDL cholesterol is significantly greater than 0