In a test of the effectiveness of garlic for lowering cholesterol, 8181 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 0.40.4 and a standard deviation of 16.216.2. Use a 0.010.01 significance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 00. 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. What are the null and alternative hypotheses?

With garlic treatment, the mean change in LDL cholesterol is not greater than 0.

Step-by-step explanation:

The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

In this case a paired t-test is used to determine the effectiveness of garlic for lowering cholesterol.

A random sample of 81 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment.

The hypothesis for the test can be defined as follows:

H₀: With garlic treatment, the mean change in LDL cholesterol is not greater than 0, i.e. d ≤ 0.

Hₐ: With garlic treatment, the mean change in LDL cholesterol is greater than 0, i.e. d > 0.

The information provided is:

Compute the test statistic value as follows:

The test statistic value is 0.22.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

Compute the p-value of the test as follows:

*Use a t-table.

The p-value of the test is 0.4132.

p-value= 0.4132 > α = 0.01

The null hypothesis was failed to be rejected.

Thus, it can be concluded that with garlic treatment, the mean change in LDL cholesterol is not greater than 0.

each side has a different length.  

step-by-step explanation: