It is desired to estimate the mean total compensation of CEOs in the Service ind

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? 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. We are 95% confident that the mean of the sampled CEOs falls in the interval $2.181.260 to $5.836.180. 95% of the sampled total compensation values between $2.181.260 and $5.836.180. 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.

Explanation / Answer

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval

We are 95% confident that the mean of the sampled CEOs falls in the interval $2181260 to $5836180

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