8. In a psychology journal, researchers reported that a chief executive officer\

Question

8. In a psychology journal, 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 computer analyzing a photo of the CEO's face) had a mean of x=2.07 and a standard deviation of s= 0.17. Use this information to complete parts a and b below the mean facial WHR for all CEOs at publicly traded a. Find and interpret a 90% confidence interval for Fortune 500 firms (Round to three decimal places as needed.) 0 A. The 90% confidence interval for mean facial WHR indicates that the true mean facial WHR for the O B. The 90% confidence interval for mean facial WHR score indicates that 90% of CEOs in the ° C. The 90% confidence interval for mean facial WHR indicates that 90% of all CEOs at publicly 0 D. The 90% confidence interval for mean facial WHR indicates that the true mean facial WHR for all CEOs in the sample is between and with 90% confidence sample have a WHR between and traded Fortune 500 firms have a WHR between and CEOs at publicly traded Fortune 500 firms is between 90% confidence and with 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 = 2.3. Do you recommend the use this value? 0 A. No, since the suggested value of does not lie within the confidence interval from part a, it is not 0 B. Yes, since the suggested value of lies within the confidence interval from part a, it is reasonable ° C. Yes, since the suggested value of would be a usual value to obtain in a sample of 55 CEOs, it 0 D. No, since the suggested value of would be a usual value to obtain in a sample of 55 CEOs, it is reasonable to assume that it is the true mean facial WHR of CEOs to assume that it is the true mean facial WHR of CEOs is reasonable to assume that it is the true mean facial WHR of CEOs not reasonable to assume that it is the true mean facial WHR of CEOs

Explanation / Answer

a) The statistical software output for this problem is:

One sample T summary confidence interval:
: Mean of population

90% confidence interval results:

Hence,

90% confidence interval will be:

Option D; 2.032; 2.108

b) Option A is correct.

Mean Sample Mean Std. Err. DF L. Limit U. Limit 2.07 0.022922795 54 2.0316372 2.1083628

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