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It is desired to estimate the mean total compensation of CEOs in the service industry. Data were randomly collected from 180 CEOs, and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct?

A. 95% of the sampled total compensation values fell between $2,181,260 and $5,836,180.

B. We are 95% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to $5,836,180.

C. In the population of service industry CEOs, 95% of them will have total compensations that fall in the interval $2,181,260 to $5,836,180.

D. We are 95% confident that the mean total compensation for all CEOs in the service industry falls in the interval $2,181,260 to $5,836,180.

Answer :

The mean total compensation for all CEOs in the service industry falls in the interval 2,181,260 to 5,836,180

The correct interpretation of the given confidence interval is:
"We are 95% confident that the mean total compensation for all CEOs in the service industry falls in the interval 2,181,260 to 5,836,180."

Here is a step-by-step explanation:
1. A confidence interval is a range of values that is likely to contain the true population parameter, in this case, the mean total compensation of CEOs in the service industry.

2. The given confidence interval (2,181,260, 5,836,180) was calculated from randomly collected data from 180 CEOs.

3. The confidence level is stated to be 95%, which means that if we were to repeat the sampling process multiple times, 95% of the confidence intervals constructed would capture the true population mean.

4. In this case, the confidence interval tells us that there is a 95% chance that the true mean total compensation of all CEOs in the service industry falls between 2,181,260 and 5,836,180.

5. It is important to note that the confidence interval does not provide information about individual CEOs' compensations. Instead, it provides a range within which we can be reasonably confident that the true mean lies.

Overall, the mean total compensation for all CEOs in the service industry falls in the interval 2,181,260 to 5,836,180 accurately reflects the information provided in the question.

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