Question

he population standard deviation for the heights of dogs, in inches, in a city is 6.5 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.

Answer 1

Solution

standard deviation =   =6.5

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 = Z0.025 = 1.960

sample size = n = [Z/2* / E] 2

n = ( 1.960* 6.5 /2 )2

n =40.5769

Sample size = n =41