Final answer:
To analyze the effectiveness of a new drug for reducing cholesterol, a paired t-test is performed, comparing pre- and post-drug cholesterol levels. The null hypothesis states no effect, while the alternative suggests a decrease. A p-value greater than the alpha level of 0.05 indicates insufficient evidence of the drug's effectiveness.
Step-by-step explanation:
When a doctor believes he has found a new drug to significantly reduce cholesterol, we can analyze its effectiveness through a hypothesis test. To begin, we state the null hypothesis (H0): there is no difference in cholesterol levels before and after taking the drug. The alternative hypothesis (Ha) is that there is a significant decrease in cholesterol levels after taking the drug.
The appropriate test for this scenario is a paired t-test, as we have before-and-after measurements for the same individuals. To calculate the test statistic, we first find the differences between each person's cholesterol levels before and after the drug. Then, we find the mean of these differences, the standard deviation, and use these to calculate the t-statistic.
Using the provided data, the test statistic (t) is calculated with the differences in cholesterol levels before and after taking the drug. Once we have the t-value, we compare it against the t-distribution for 7 degrees of freedom (n-1, where n is the number of paired observations) to find the p-value.
Comparing the p-value to the alpha level of 0.05, if the p-value is less than 0.05, we reject the null hypothesis, meaning the drug likely has an effect on lowering cholesterol. If the p-value is larger than 0.05, we do not have enough evidence to reject the null hypothesis, suggesting the drug may not be effective.
In a situation where the p-value reported is 0.1494, which is greater than the alpha of 0.05, we conclude that there is insufficient evidence to conclude that the medication lowered cholesterol levels after the treatment period.