Exhibit 22-3
From a population of size 600, a simple random sample of size 58 is selected. The sample mean is 400, and the sample standard deviation is 40.
-Refer to Exhibit 22-3. The population total is
A)3,944
B)16,000
C)240,000
D)24,000

Question

Quizplus · Accepted Answer

The formula to calculate population total is:
Population Total = Sample Mean x Population Size
Here, we have the sample mean (400) and we know that the sample size is 58, but we do not know the population size. However, we are given that the population size is 600. Therefore, we can set up a proportion:
Sample Size / Population Size = Sample Mean / Population Mean
58 / 600 = 400 / Population Mean
Population Mean = (400 x 600) / 58 = 4,129.31
Population Total = Sample Mean x Population Size = 400 x 4,129.31 = 1,651,724
Rounding this to the nearest thousand gives us a population total of 1,652,000, which is closest to choice C (240,000).

Exhibit 22-3 From a Population of Size 600, a Simple Random Sample