A researcher takes a sample of 500 executives in large U.S. corporations. In the sample the average annual income for the executives is $500,000. Our researcher estimates the value of the standard error to be $10,000. Complete the following statements: "The sample result was $500,000 with a margin of error of ___________ and a level of confidence of 95 percent."
A) $1,000
B) $10,000
C) $20,000
D) $480,000

Question

Quizplus · Accepted Answer

The margin of error can be computed as the product of the critical value and the standard error.

Since the level of confidence is 95 percent, the critical value is approximately 1.96 (from a standard normal distribution table).

Therefore, the margin of error is:

1.96 * $10,000 = $19,600

Thus, the complete statement is:

"The sample result was $500,000 with a margin of error of $19,600 and a level of confidence of 95 percent."

Therefore, the correct choice is C ($20,000), which is the closest option to the calculated margin of error.

A Researcher Takes a Sample of 500 Executives in Large