A study on corporate leadership compares the heights of CEO candidates and their opponents in 100 100 board elections. In the study, it was found that in 60 60 of the elections, the CEO candidate was taller than their opponent. The remaining 40 40 elections had the opponent taller than the CEO candidate. Construct a 95 % 95\% confidence interval for the true proportion of CEO candidates who are taller than their opponents. Based on the results, does it appear that greater height is an advantage for CEO candidates? Why or why not?

32.12 % < p < 48.17 % 32.12\%<p<48.17\% No. Greater height is not an advantage for CEO candidates since the entire confidence interval is below 50 % 50\% .

61.02 % < p < 72.18 % 61.02\%<p<72.18\% Yes, we can conclude that greater height is likely an advantage for CEO candidates since the entire confidence interval is above 60 % 60\% .

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Problem 29Multiple Choice

A study on corporate leadership compares the heights of CEO candidates and their opponents in $100$ board elections. In the study, it was found that in $60$ of the elections, the CEO candidate was taller than their opponent. The remaining $40$ elections had the opponent taller than the CEO candidate. Construct a $95 percent sign$ confidence interval for the true proportion of CEO candidates who are taller than their opponents. Based on the results, does it appear that greater height is an advantage for CEO candidates? Why or why not?

$32.12 percent sign is less than p is less than 48.17 percent sign$ .

$61.02 percent sign is less than p is less than 72.18 percent sign$ .

$50.40\%<p<69.60\%$

Yes, we can conclude that greater height is an advantage for CEO candidates since the entire confidence interval is above $50 percent sign$ .

$52.47 percent sign is less than p is less than 65.49 percent sign$ $50\%$ .

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