Answered: A psychology student conducted a study…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A psychology student conducted a study on using a chief executive officer's facial structure to predict a firm's financial performance. The facial width-to-height ratio (WHR) for each in a sample of

CEOs at publicly traded firms was determined. The sample resulted in

x=2.23

and

s=0.35.

The student wants to predict the financial performance of a firm based on the value of the true mean facial WHR of CEOs. The student wants to use the value of

μ=2.1.

Do you recommend he use this value? Conduct a test of hypothesis for

to help you answer the question. Specify all the elements of the test, including

H0,

Ha,

test statistic, p-value, and your conclusion. Test at

α=0.01.

### Hypothesis Testing for CEO Facial WHR and Firm Financial Performance

A psychology student conducted a study on using a chief executive officer’s facial structure to predict a firm’s financial performance. The facial width-to-height ratio (WHR) for each in a sample of 47 CEOs at publicly traded firms was determined. The sample resulted in x̄ = 2.23 and s = 0.35. The student wants to predict the financial performance of a firm based on the value of the true mean facial WHR of CEOs. The student wants to use the value of μ = 2.1. Do you recommend he use this value? Conduct a test of hypothesis for μ to help you answer the question. Specify all the elements of the test, including $ H_0 $, $ H_a $, test statistic, p-value, and your conclusion. Test at $ \alpha = 0.01 $.

1. **What are the null and alternative hypotheses?**
- A. $ H_0: \mu = 2.1 $
$ H_a: \mu < 2.1 $
- B. $ H_0: \mu = 2.1 $
$ H_a: \mu > 2.1 $
- C. $ H_0: \mu = 2.1 $
$ H_a: \mu \neq 2.1 $
- D. $ H_0: \mu = 2.1 $
$ H_a: \mu \neq 2.1 $

2. **What is the value of the test statistic?**

$ z = $ ___ (Round to two decimal places as needed.)

3. **Find the p-value.**

p-value = ___ (Round to three decimal places as needed.)

4. **What is the appropriate conclusion at $ \alpha = 0.01 $?**
- A. Reject $ H_0 $. There is sufficient evidence to conclude the true mean facial WHR is not 2.1.
- B. Do not reject $ H_0 $. There is insufficient evidence to conclude that the true mean facial WHR is not 2.1.
- C. Reject $ H_0 $. There is insufficient evidence to conclude the true mean facial WHR is not 2.1.
- D. Do not

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