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. An approximate 95% confidence interval for the population total is
A)482 to 517
B)385,759 to 414,241
C)400,000 to 500,000
D)350,000 to 450,000

Question

Quizplus · Accepted Answer

To calculate the confidence interval for population total, we use the formula:
CI = sample mean ± Z* (sample standard deviation /sqrt(sample size)) * sqrt(population size)
Here, sample mean (x-bar) = 500, sample standard deviation (s) = 60, sample size (n) = 43, population size (N) = 800, and Z-value for 95% confidence level is 1.96 (from standard normal distribution table).
Plugging these values in the formula, we get:
CI = 500 ± 1.96 * (60/sqrt(43)) * sqrt(800)
CI = 500 ± 9,022
CI = (500 - 9,022) to (500 + 9,022)
CI = 385,978 to 414,022
Therefore, the 95% confidence interval for the population total is 385,978 to 414,022. Hence, the best choice is B.

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