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 mean is
A)482.2 to 517.8
B)440.0 to 560.0
C)500.0 to 560.0
D)440.0 to 500.0

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for the population mean as follows:

Confidence interval = sample mean ± (critical value (based on the level of confidence) × standard error of the mean)

Since the population standard deviation is unknown, we need to use the t-distribution and the degrees of freedom = n-1 = 42.

The critical value for a 95% confidence interval with 42 degrees of freedom is approximately 2.021 (found in t-table or using a calculator).

The standard error of the mean can be calculated as:

standard error of the mean = sample standard deviation / sqrt(sample size)
standard error of the mean = 60 / sqrt(43)
standard error of the mean ≈ 9.16

Therefore, the 95% confidence interval can be calculated as:

Confidence interval = 500 ± (2.021 × 9.16)
Confidence interval ≈ (482.2, 517.8)

Thus, the best choice is A) 482.2 to 517.8.

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