Question

A student surveys a random sample of 60 undergraduates and records their average number of drinks (¯x) consumed over the past two weeks. Based on previous surveys, the student believes that the standard deviation of drinks per week in the undergraduate population equals 7. The student aims to reduce the standard error by increasing the sample size. (a) If the student’s beliefs are correct, what is the standard error of ¯x? (b) How many students would the student have to survey to cut the standard error in half?

Answer 1

(A) standard error =

where

this implies

(B) To reduce the standard error to half, lets divide the standard error by 2

this implies, 0.9037/2 = 0.45185

putting 0.45185 in the standard error equation and solve for new value of n

solving for n by cross multiplication

squaring both sides

rounding it off to nearest whole number, n = 240

240 students are required to cut the standard error in half