Question

Lecture19: Problem 4 Previous Problem List Next (1 point) 1Q tests are designed so that the mean is 100 points and the standard deviation is 15 points for the entire adult population. What is the minimum sample size needed to estimate the average IQ of all Stat 200 students to within 3 points with 96% confidence? Note: You can get a new version of this problem after the due date. Preview My Answers Submit Answers

Answer 1

Solution :

Given that,

Population standard deviation = $\sigma$ = 15

Margin of error = E = 3

At 96% confidence level the z is ,

$\alpha$ = 1 - 96% = 1 - 0.96= 0.04

$\alpha$ / 2 = 0.04 / 2 = 0.02

Z_$\alpha$/2 = Z_0.02 = 2.054

sample size = n = (Z_$\alpha$/2* $\sigma$ / E) ²

n = (2.054* 15/ 3)²

n = 105.47

n = 106

Sample size = 106