Question

The population standard deviation for the heights of dogs, in inches, in a city is 7.8 inches. If we want to be 95% 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	z0.05	z0.04	z0.025	z0.01	z0.005
1.282	1.645	1.751	1.960	2.326	2.576

Use the table above for the z-score, and be sure to round up to the nearest integer.

Provide your answer below:

Answer 1

Solution :

Given that,

Population standard deviation = = 7.8

Margin of error = E = 2

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

sample size = n = (Z_/2* / E) ²

n = (1.960 * 7.8/ 2)²

n = 58.43

n = 59

Sample size = 59

The minimum sample size that can be taken is 59.