Question

It is desired to estimate the mean total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct?

A) We are 95% confident that the mean total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180.
B) 95% of the sampled total compensation values fell between $2,181,260 and $5,836,180.
C) We are 95% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to $5,836,180.
D) 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.

Answer 1

The correct interpretation of the 95% confidence interval for the mean total compensation of CEOs in the Service industry is:

A) We are 95% confident that the mean total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180.

The correct interpretation of the 95% confidence interval for the mean total compensation of CEOs in the Service industry is:

A) We are 95% confident that the mean total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180.

This interpretation aligns with the concept of a confidence interval, which expresses the range within which we can reasonably estimate the population parameter (in this case, the mean total compensation of all CEOs in the Service industry) based on sample data.