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 26 points. (a) Raina wants to use a 90% condence interval. How large a sample should she collect?
(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.
(1) smaller since Luke has a higher level of confidence in his results than Raina
(2) smaller because higher degrees of confidence require smaller margins of error
(3) larger higher degrees of confidence require larger margins of error
(c) Calculate the minimum required sample size for Luke.