SAT scores of students at an Ivy League college are distributed with a standard deviation of 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 25 points.
(a) Raina wants to use a 90% condence interval. How large a sample should she collect?
Raina should sample at least people.
(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.
- smaller because higher degrees of confidence require smaller margins of error
- smaller since Luke has a higher level of confidence in his results than Raina
- larger higher degrees of confidence require larger margins of error
(c) Calculate the minimum required sample size for Luke.
Luke should sample at least people.