Question

Suppose that a pharmaceutical company is interested in testing their new cholesterol medication and recruited 24 adults with high blood pressures, where half of them were given the new drug and the other half were given the old drug. Then the reduction in LDL cholesterol level (unit: mg/dL) was measured after 6 months. Summary statistics of the amount of reduction are shown below.

NOTE: Not all outputs given above are useful

	n	x	s
New Drug	12	32	23
Old Drug	12	19	17
Difference (New Drug - Old Drug)	12	13	27

Answer the following questions. If necessary, round your answer to four decimal places.

(a) If the company wishes to test if the average reduction in LDL cholesterol level is higher for the new drug, what would be the most appropriate test to conduct?

The two-sample t-test (unequal variances)The paired t-test for a difference in means    The one-sample t-test for a population mean

(b) Conduct the appropriate test. Use the significance level α = 0.05.

STEP 1: Set up null and alternative hypotheses using statistical terms only.

H₀:  --- μD μ1 - μ2 μ   --- > = < ≠   
H_A:  --- μ μD μ1 - μ2   --- < ≠  > =   

1. μ_D represents the population mean difference between reduction from the new drug and the new old drug (New Drug - Old Drug).
2. μ₁ represents the population mean reduction from the new drug
3. μ₂ represents the population mean reduction from the old drug.

STEP 2: Check all conditions. Make sure your answer is in context of the problem.

STEP 3: Calculate the test-statistic and p-value. If necessary, round your answers to four decimal places.

df =  
t =
< p-value <

STEP 4: State the conclusion in statistical terms.

Reject the null hypothesis.Fail to reject the null hypothesis.    

State the conclusion in problem context.

Answer 1

(a) The paired t-test for a difference in means.

STEP 2: The dependent variable is the reduction in LDL cholesterol level. It is continuous, it should be approximately normally distributed, it should not contain any outliers and the observations are independent of one another.
STEP 4: Fail to reject the null hypothesis, since the p-value is greater than the 0.05 significance level.
We conclude that there is not enough evidence to suggest that the average reduction in LDL cholesterol level is higher for the new drug.