The standard deviation of SAT scores for students at a particular Ivy League college is 250 points. Two statistics students, Raina and Luke, want to estimate the average SAT score of students at this college as part of a class project. They want their margin of error to be no more than 24 points. (a) Raina wants to use a 90% confidence interval. How large a sample should she collect? (Round your answer to the nearest whole number.) students (b) Luke wants to use a 99% condence interval. Without calculating the actual sample size, determine whether his sample should be larger or smaller than Raina's, and explain your reasoning. If Luke had the same sample size as Raina but used a higher condence level, he would end up with a 4 interval. Therefore, to keep the width of this interval the same as Raina's, he will need a ./ sample size. (c) Calculate the minimum required sample size for Luke. (Round your answer to the nearest whole number.) |:| students