Exhibit 21-2
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 21-2. 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 find an approximate 95% confidence interval for the population total, we need to use the formula:
Estimate ± (Critical value) × (Standard error of estimate)
where the estimate is the sample mean multiplied by the population size, the critical value is obtained from the t-distribution table with (n-1) degrees of freedom and a 95% confidence level, and the standard error of estimate is given by the formula:
Sample standard deviation / sqrt(n)
Plugging in the values, we get:
Estimate = 500 × 800 = 400,000
Standard error of estimate = 60 / sqrt(43) ≈ 9.17
Using a t-distribution table with 42 degrees of freedom (n-1), we find the critical value to be 2.021. 
Therefore, the 95% confidence interval is:
400,000 ± 2.021 × 9.17
= 400,000 ± 18,554.5
= (385,445.5, 414,554.5)
which corresponds to choice B.

Exhibit 21-2 A Simple Random Sample of 43 Elements Has Been Selected