Question

a pharmaceutical company needs to know if its new cholesterol drug, praxor, is effective at lowering cholesterol levels. it believes that people who take praxor will average a greater decrease in cholesterol level than people taking a placebo. after the experiment is complete, the researchers find that the 44 participants in the treatment group lowered their cholesterol levels by a mean of 20.7 points with a standard deviation of 5.1 points. the 34 participants in the control group lowered their cholesterol levels by a mean of 18.6 points with a standard deviation of 1.3 points. assume that the population variances are not equal and test the companys claim at the 0.02 level. let the treatment group be population 1 and let the control group be population 2.
step 3 of 3: draw a conclusion and interpret the decision.
answer
we fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.02 level of significance to support the companys claim that people who take the drug will average a greater decrease in cholesterol level than people taking a placebo.
we reject the null hypothesis and conclude that there is sufficient evidence at a 0.02 level of significance to support the companys claim that people who take the drug will average a greater decrease in cholesterol level than people taking a placebo.
we reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance to support the companys claim that people who take the drug will average a greater decrease in cholesterol level than people taking a placebo.
we fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance to support the companys claim that people who take the drug will average a greater decrease in cholesterol level than people taking a placebo.

Explanation:

Step1: Recall hypothesis - testing conclusion rules

In hypothesis - testing, if the p - value is less than the significance level ($\alpha$), we reject the null hypothesis. If the p - value is greater than $\alpha$, we fail to reject the null hypothesis. Here, $\alpha = 0.02$.

Step2: Analyze the claim

The company's claim is that people who take the drug (Population 1) will average a greater decrease in cholesterol level than people taking a placebo (Population 2). The null hypothesis $H_0:\mu_1-\mu_2\leq0$ and the alternative hypothesis $H_1:\mu_1 - \mu_2>0$.

Step3: Make a conclusion

If we reject the null hypothesis, it means there is sufficient evidence to support the company's claim. If we fail to reject the null hypothesis, it means there is insufficient evidence to support the claim. Since we are testing at the 0.02 level of significance, we need to calculate the test - statistic and its corresponding p - value (not shown in this step - 3 only part but assumed to be calculated previously). If the p - value < 0.02, we reject $H_0$. If p - value $\geq0.02$, we fail to reject $H_0$.

Answer:

We reject the null hypothesis and conclude that there is sufficient evidence at a 0.02 level of significance to support the company's claim that people who take the drug will average a greater decrease in cholesterol level than people taking a placebo.