Question

Suppose you want to construct a 99% confidence interval for the average height of US

males above the age of 20. Based on past studies you think the standard deviation of

heights for this population is around 6 inches. How large a sample should you gather to

ensure that your confidence interval has a width no greater than 1 inch?

Answer 1

Solution :

Given that,

Population standard deviation = = 6

Margin of error = E = width / 2 = 0.5

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

sample size = n = (Z/2* / E) 2

n = (2.576 * 6/ 0.5)2

n = 955.55

n = 956

Sample size = 956