Example 2: Suppose that there is a new "smart pill" on the market that claims that it will improve ACT scores if taken the day before the test. To test the validity of this claim, we set up a randomized comparative experiment. 18 students volunteer for the experiment. 10 students chosen at random are given the "smart pill" the day before the test and 8 students chosen at random are given a placebo the day before the test. We then record their scores. Assume distribution of ACT scores are normal. "smart pill" 23 28 19 22 27 18 23 28 21 23 placebo 21 29 25 19 17 21 24 21 Is this a matched pairs design or a two sample problem? two sample Does it make sense to use differences? Construct and interpret a 90% confidence interval for the difference in mean scores