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Problem 15 Easy Difficulty

CEO compensation A sample of 20 CEOs from the Forbes 500 shows total annual compensations ranging from a minimum of $0.1 to $62.24 million. The average for these 20 CEOs is $7.946 million. Here’s a histogram:
Graph cannot copy
Based on these data, a computer program found that a 95% confidence interval for the mean annual compensation of all Forbes 500 CEOs is (1.69, 14.20) $ million. Why should you be hesitant to trust this confidence interval?

Answer

a. Increases
b. Yes, margin of error will decrease if the confidence level is decreased.
c. Yes

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Video Transcript

when a problem gives you a history. Graham, that looks like this. Um are, uh, using this confidence Intervals, um means that one of things have to assume is other data is normally distributed. So it gave us a confidence interval. That's like for this, Um, so because it's we have this one or maybe two outliers way out to the right. If we can eliminate those outlines, our confidence interval, I think, would give us a much closer mean to the actual mode of this data where the median of the state of which would be reflected by this pillar. So because our confidence interval, it became so wide because the out liar, I would just say, Be careful of that outlier. Um And so that's why I would be hesitant to trust his confidence intervals because of that large outlier. Okay, thank you very much.