we are interested in comparing the mean costs of electrical

we are interested in comparing the mean costs of electrical energy produced by nuclear and coal powered electrical power plants. Pilot studies have indicated the variation in the costs associated with the two types of plants are s_n= $.224 and s_c= $ .20.How many plants of each type should be sampled in order to estimate the difference mean costs with a 95% confidence interval to within $.01?

Solution

sn = 0.224 and sc = 0.20

Let sample sizes be n1 and n2

SE = 0.224/rtn1 + 0.20/rtn2

Margin of error = z alpha/2 (SE)

For 95% z = 1.96

Hence 1.96(0.224/rtn1 + 0.20/rtn2) = 0.01

As there is one equation and two variables assume n1 = n2

Then we have

0.424/rtn1 = 0.01/1.96 = 0.0051

Or rt n1 = 8.313

n1 =69.111

or n >70 for each sample.