Question

1. Assume the population standard deviation of the student scores in survey is 7.5. Find the sample size needed to achieve a 3.1 points margin of error at 95% confidence level.

Answer 1

Solution :

Given that,

Population standard deviation = = 7.5

Margin of error = E = 3.1

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = Z_0.025 = 1.96  

sample size = n = [Z_/2* / E] ²

n = [1.96 * 7.5 / 3.1 ]²

n = 22.48

Sample size = n = 23