Answer to Question #320138 in Statistics and Probability for Ali De Austria

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