Question

The heights (in inches) of the students on a campus have a normal distribution with a population standard deviation σ =5 inches. Suppose we want to construct a 95% confidence interval for the population mean height and have it accurate to within 0.5 inches. What is the required minimum sample size?

Answer 1

Solution :

Given that,

standard deviation = = 5

margin of error = E = 0.5

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 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 5) / 0.5)²

= 384.1 = 384

Sample size = 384