A sample of 20 CEOs shows total annual compensations ranging from a minimum of $

Question

A sample of 20 CEOs shows total annual compensations ranging from a minimum of $0.1 to $62.49 million. The average for these 20 CEOs is $17.121 million. The histogram and boxplot are shown above. Based on these data, a computer program found that a 95% confidence interval for the mean annual compensation of all CEOs is (- 7.86, 42.11) $M. Why should you be hesitant to trust this confidence interval? Choose the correct answer below: A. The assumptions and conditions for a t-interval are not met. The distribution is bimodal. B. The assumptions and conditions for a t-interval are not met. The distribution is too skewed for a sample size of only 20. C. The assumptions and conditions for a t-internal are not met. The distribution has a large outlier that is pulling the mean higher. D. The assumptions and conditions for a t-interval are met. The confidence interval is satisfactory.

Explanation / Answer

Option C.

This is because of the fact that while constructing a t interval one should keep in mind that there is no large outlier. If there is a large outlier then t interval constructed will not be that conclusive. This is because since a large outlier will tend to pull the mean higher,hence it will effect highly the t interval that will be constructed. As it is evident from the histogram as well as the boxplot that there is a large outlier,hence we are hesitant to trust the confidence interval.

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