In Psychological Science (Vol. 22, 2011), researchers reported that a chief executive officer's facial structure can be used to predict a firm's financial performance. The study involved measuring the facial width to-height ratio (WHR) for each in a sample of 55 CEOs at publicly traded Fortune 500 firms. These WHR values (determined by a computer analyzing a photo of the CEO's face) had a mean of x̅ = 1.96 and a standard deviation of s = .15.
a. Find and interpret a 95% confidence interval for μ, the mean facial WHR for all CEOs at publicly traded Fortune 500 firms.
b. The researchers found that CEOs with wider faces (relative to height) tended to be associated with firms that had greater financial performance. They based their inference on an equation that uses facial WHR to predict financial performance. Suppose an analyst wants to predict the financial performance of a Fortune 500 firm based on the value of the true mean facial WHR of CEOs. The analyst wants to use the value of μ = 2.2. Do you recommend he use this value?