Question

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 since Luke has a higher level of confidence in his results than Raina

smaller because higher degrees of confidence require smaller margins of error

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.

Answer 1

smaller since Luke has a higher level of confidence in his results than Raina

Explanation:

Given that SAT scores of students at an Ivy League college are distributed with a standard deviation of 250 points

Raina wants to get margin of error <25

90% confidence level critical value = 1.645

If n is the sample size Raina selected then

`1.645*(250)/(√(n) ) \leq 25\\√(n)\geq 16.45\\n\geq 270.6025\\n\geq 271`

/atleast 271 should be sample size for Raina

b) Luke for 99% confidence here critical value would be 2.58 instead of 1.645

Hence sample size should be smaller to get the same margin of error.

smaller since Luke has a higher level of confidence in his results than Raina