Exhibit 22-2
A simple random sample of 43 elements has been selected from a population of size 800. The sample mean is 500, and the sample standard deviation is 60.
-Refer to Exhibit 22-2. The population total is
A)34,400
B)21,500
C)400,000
D)500,000

Question

Quizplus · Accepted Answer

To find the population total, we can use the formula: population total = sample mean * population size. Rearranging this equation gives us population size = population total / sample mean. Plugging in the values given, we get population size = population total / 500. To solve for population total, we need to find population size. The formula for standard error of the mean is: standard deviation / square root of sample size. Plugging in the values given, we get standard error of the mean = 60 / sqrt(43) = 9.16. We can use this to construct a 95% confidence interval for the population mean by adding and subtracting 1.96 times the standard error of the mean from the sample mean. This gives us an interval of 500 +/- 1.96*9.16, or (482.7, 517.3). To calculate population size, we can use the lower and upper bounds of this interval to get two estimates of population size: 482.7*n and 517.3*n, where n is the population size. Since we know n = 800, we can solve for the population total by plugging this into our two equations: 482.7*800 = 386,160 and 517.3*800 = 413,840. Taking the average of these two estimates gives us a population total of (386,160 + 413,840) / 2 = 400,000, which is answer choice C.

Exhibit 22-2 A Simple Random Sample of 43 Elements Has Been Selected