**Is CEO Compensation Related to a Company's Performance?**To test whether CEO compensation and a company's stock performance are related, a financial analyst collected data on 15 randomly selected, publicly traded companies. The analyst examined two variables: the percent change in stock price over the past five years (denoted as $ x $) and the percent change in CEO compensation over the past five years (denoted as $ y $). For these 15 companies, the least-squares regression equation relating the two variables was $ \hat{y} = -0.161 + 0.039x $, and the standard error of the slope of this least-squares regression line was approximately 0.018.Using this information, perform a hypothesis test for a significant linear relationship between these two variables regarding the population slope $ \beta_1 $. Assume that the variable $ y $ follows a normal distribution for each value of $ x $ and that the other regression assumptions are satisfied. Use the 0.10 level of significance and perform a two-tailed test. Complete the parts below:- (a) State the null hypothesis $ H_0 $ and the alternative hypothesis $ H_1 $. $ H_0 :\ $ ( ) $ H_1 :\ $ ( )- (b) Determine the type of test statistic to use. (Choose one)- (c) Find the value of the test statistic. (Round to three or more decimal places.)- (d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.)**Note:** If necessary, consult a list of formulas.**Graphical Explanation:**- The regression plot would typically show the relationship between $ x $ (percent change in stock price) and $ y $ (percent change in CEO compensation) with the regression line based on the given equation, indicating any correlation trends.- The equation $ \hat{y} = -0.161 + 0.039x $ can be used to predict changes in CEO compensation based on stock price changes.- Standard errors help determine the reliability of the slope estimate, which is tested in hypothesis testing to see if there is a significant relationship between the variables. ### Statistical Hypothesis Testing: An OverviewIn this exercise, we will perform a two-tailed test to determine the linear relationship between two variables. Here are the steps and components involved:#### (a) Hypotheses Formulation- **Null Hypothesis ($ H_0 $)**: The statement assuming no effect or no difference.- **Alternative Hypothesis ($ H_1 $)**: The statement we aim to prove, indicating an effect or difference.#### (b) Test Statistic- **Type of Test Statistic**: Select the appropriate test statistic to analyze the data. Choices may include t-test, z-test, chi-square, etc., depending on the data and hypotheses.#### (c) Calculating the Test Statistic- **Value of the Test Statistic**: Calculate this value from the data, rounding to three or more decimal places for precision.#### (d) Critical Values- **Critical Values at 0.10 Level of Significance**: Determine the threshold values for the test statistic, rounded to three or more decimal places, to decide whether to reject $ H_0 $.#### (e) Conclusion- **Conclusion Based on the 0.10 Level**: Analyze if there is a significant linear relationship between the percent change in stock price and CEO compensation over the past five years. - Options: **Yes** or **No**### Symbols and Calculator FunctionsThe diagram on the right provides mathematical symbols and tools for calculations, such as mean ($\bar{x}$), standard deviation ($\sigma$), greater than or less than ($>, <$), and equality/inequality ($=, \neq$).Remember: When filling in the blanks or selecting from options, ensure the correctness based on the problem's context and available data. Make well-informed decisions using statistical principles.

Given , Regression equation : y^ =-0.161 +0.039x Slope = b1 = 0.039 y-intercept = b0 = -0.161…

Answered: Is CEO compensation related to a…

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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