Suppose an SAT tutoring company really can improve SAT scores by 10 points, on average. A competing company, however, uses a more intense tutoring approach and really can improve SAT scores by 15 points, on average. Suppose you've been hired by both companies to test their claims that their tutoring improves SAT scores. For both companies, you will collect a random sample of high school students to undergo tutoring. With both resulting samples, you will test the hypothesis that the mean improvement is more than 0. Suppose it is important to keep the power of both studies at 80%. Will you use the same sample size for both studies? If so, explain why you can. If not, which study would require the larger sample size, and why? Assume that both samples of students will be drawn from the same population.