Question

Chapter 6, Section 2-CI, Exercise 110

What Influences the Sample Size Needed?

In this exercise, we examine the effect of the margin of error on determining the sample size needed.

Find the sample size needed to give a margin of error within ± 2 with 99% confidence. With 95% confidence. With 90% confidence. Assume that we use ά =30 as out estimate of the standard deviation in each case.

Round your answers up to the nearest integer.

99% n= _______
95%: n= _______
90% : n= _______

Answer 1

Solution :

Given that,

Population standard deviation = = 30

Margin of error = E = 2

(a) 99%

Z_/2 = 2.576

sample size = n = [Z_/2* / E] ²

n = [2.576 * 30 / 2]²

n = 1493.04

Sample size = n = 1494

(b)

95%

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [1.96 * 30 / 2]²

n = 864.36

Sample size = n = 865

(c)

90%

Z_/2 = 1.645

sample size = n = [Z_/2* / E] ²

n = [1.645 * 30 / 2]²

n = 608.8

Sample size = n = 609