Question

The population standard deviation for the heights of dogs in inches in a city is 3.9 inches. If we want to be 90% confident that the sample mean is within 2 inches of the true population mean. What is the minimum sample size that can be taken?

Z0.10

1.282

Z0.05

1.645

Z0.025

1.960

Z.0.01

2.326

Z0.005

2.576

Answer 1

Solution :

Given that,

Population standard deviation = = 3.9

Margin of error = E = 2

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

sample size = n = (Z_/2* / E) ²

n = (1.645 * 3.9/ 2)²

n = 10.2897

n = 11

Sample size = 11