Question

Computing Appropriate Sample Size Using the Length of the Interval

A. Determine the minimum sample size for each of the following:

a. 95% confidence level, E = 5.8 , $\sigma$ = 40

b. 96% confidence level, E =6, $\sigma$ = 55

c. 99% confidence level, E = 6.5, $\sigma$ = 65

Answer 1

a)

n=$\frac{Z^2\cdot s^2}{E ^2}$

Z=1.96

s=40

E=5.8

n=$\frac{1.96^2\cdot 40^2}{5.8^2}$ =182.7158

Therefore the required sample size is 183

b)

n=$\frac{Z^2\cdot s^2}{E ^2}$

Z=2.05

s=55

E=6

n=$\frac{2.05^2\cdot 55^2}{6^2}$ =353.1267

Thus the required sample size is 353

c)

n=$\frac{Z^2\cdot s^2}{E ^2}$

Z=2.58

s=65

E=6.5

n=$\frac{2.58^2\cdot 65^2}{6.5^2}$

n=665.64

The required sample size is 666