a coal company wants to determine a 95 confidence interval e

a coal company wants to determine a 95% confidence interval estimate for the average daily tonnage of coal that they mine. Assuming that the company reports that the standard deviation of daily out-put is 100 tons, how many days should they sample so that the margin of error will be 20 tons or less?

Solution

standard deviation of daily out-put s = 100 tons

margin of error E = +20

For alpha = 0.05, z = +1.96

Let sample size be n

n = (z * s / E)^2 = (1.96 * 100 / 20)^2 = 96.04

As the sample size should be an integer value, and greater than the above value 96.04, the result must be rounded UP to the next highest integer.

Answer: Required sample size = 97