It is desired to estimate the average total compensation of CEOs in the publishing industry. Data were randomly collected from 18 CEOs and 95% confidence interval was calculated to be ($2,190,000, $4,720,000). Based on the interval above, do you believe the actual average total compensation of CEOs in the publishing industry could be $3,000,000. a. Yes, and I am sure of that. b. Yes, and I am 95% confident of that. c. No, and I am sure of that. d. No, and I am 95% confident of that.
Mathematics · College · Thu Feb 04 2021
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b. Yes, and I am 95% confident of that.
The confidence interval provided is from $2,190,000 to $4,720,000, which suggests that we can be 95% confident that the true mean (average) total compensation of CEOs in the publishing industry is between these two values. Since $3,000,000 lies within this range, it is reasonable to believe that the actual average could be $3,000,000, and this belief is backed up with 95% confidence. However, it is important to remember that the 95% confidence level does not guarantee that the actual average is $3,000,000; it simply indicates that there is a 95% probability that the true average falls within the specified interval.