It is desired to estimate the mean total compensation of CEO

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

A) 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

B) 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

C)95% of the sampled total compensation values fell between $2,181,260 and $5,181,180

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

Solution

Confidence intervals are used because a study recruits only a small sample of the overall population so by having an upper and lower confidence limit we can infer that the true population effect lies between these two points. Most studies report the 95% confidence interval (95%CI).

Interpretation of 95% confidence interval:B) 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