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GenaCL600
3 months ago
14

A journalist wants to determine the average annual salary of CEOs in the S&P 1,500. He does not have time to survey all 1,50

0 CEOs but wants to be 95% confident that his estimate is within $50,000 of the true mean. The journalist takes a preliminary sample and estimates that the standard deviation is approximately $449,300. What is the minimum number of CEOs that the journalist must survey to be within $50,000 of the true average annual salary? Remember that the z-value associated with a 95% confidence interval is 1.96.
Mathematics
1 answer:
Inessa [12.5K]3 months ago
8 0

Answer:

At least 315

Step-by-step explanation:

A journalist intends to find the average annual salary of CEOs within the S&P 1,500. Due to time constraints, a sample is used.

Standard deviation of the sample (s) = 449300

Sample size = n

Permissible margin of error = 50000

Z critical value = 1.96

Thus, 1.96 times the standard error equals 50000.

Standard error equals 25510.20

Standard deviation divided by the square root of n = 25510.20

By simplifying, we can derive:

\sqrt{n} =\frac{449300}{25510.20} =17.752\\n=315\\

Thus, the minimum sample size required is 315.

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