A scientist wants to test the effectiveness of a new drug compared to an old one. Which test do you think should she use, one-tailed or two-tailed? Explain.?

The decision to use a one-tailed or two-tailed test depends on the research question being investigated. In the case of comparing the effectiveness of a new drug to an old one, the researcher might be interested in determining whether the new drug is either better or worse than the old drug, or simply different. If the research question is formulated as whether the new drug is better than the old one, and the hypothesis is directional, then a one-tailed test should be used. In a one-tailed test, all the critical values are in one tail of the distribution, either in the positive or negative direction, depending on the direction of the hypothesis. A one-tailed test is more powerful than a two-tailed test as it concentrates all the alpha level in one direction, allowing the rejection of the null hypothesis with a smaller sample size. Therefore, if the researcher hypothesizes that the new drug is more effective than the old one, then a one-tailed test would be appropriate. On the other hand, if the researcher is interested in whether the new drug is different from the old drug, without a specific directional hypothesis, then a two-tailed test should be used. In a two-tailed test, the critical values are split equally between the positive and negative tails of the distribution. A two-tailed test is appropriate when there is no prior reason to expect a specific direction of the effect, and the researcher is interested in detecting any significant difference, whether positive or negative. In summary, the decision to use a one-tailed or two-tailed test depends on the research question and the specific hypothesis being tested.