Wite down the null and alternative hypotheses for testing

Question

Question 1:

Investors make decisions on buying or selling assets based on both their rate of return and their risk (which can be measured by the variance of the returns). The following table provides summary information about three different assets based on three independent random samples:

Asset1	Asset2	Asset3
n1 = 21	n2 = 21	n3 = 21
x1 = 5	x2 = ?	x3 = 7	ss(tota)l = 462
s1 = 0.3	s2 = 0.4	s3 = ?	x = 6

where n₁, x_i¯, and s_i are the number of observations, average rate of return and standard deviation of rates of return for each asset class respectively. Assuming the rates of return are normally distributed, answer the following questions:

a) Write down the null and alternative hypotheses for testing whetherAsset-1 is less risky than Asset-2. What is the test statistic and its distribution under the null?

b) Are there any differences between the average rates of return for the three assets? (Follow thesix steps of the test and do the hypothesis test at the 1% level of significance.)

c) What test should be used for comparing the average rates of return for the three assets if the normality assumption is not satisfied? Write down the null and alternative hypotheses for that test(you do not need to actually perform the test).

Question 2:

Increases in chief executive officer (CEO) salaries over the last decade have been debated passionately in the media and by business analysts. A researcher has considered the following model to explain the factors determining the salaries of CEOs:

ln salary =  β0 +  β1Roe + β2 lnFirmSize + β3Year + ε

where

Salary = salary of CEO of company

Roe = Return on equity, a measure of performance of a company, in percentage point eg. Roe = 4 means a return of 4 percent

FirmSize = Market value of the company

year = The number of years the person has been the CEO of the company

ln denotes natural logarithm and ε is a random error term.

Based on data from 200 companies, he has estimated the following model:

Dependent Variable: lnSalary
Method: Least Squares
Sample: 1 200
Included observations: 200

Variable	Coefficient	Std. Error	t-statistic	Prob.
C	1.1323	0.3398	3.3324	0.0005
Roe	0.9705	?	2.9678	0.0017
lnFirmSize	0.5198	0.1114	?	0.0000
Year	0.0561	0.0098	5.7327	0.0000
R-squared	?
Adjusted R-squared	?	SD of Dependent Variable		1.450
S.E. of regression	?
Sum squared resid	252.6727
Log likelihood	-731.1084
F-statistic	?

a) Calculate the following:

(i)Standard error (SE) of b₁
(ii) t-statistic of b₂ (iii) s_ε
b) Report the results of the regression and interpret the coefficient of Roe.

c) Does the salary of a CEO depend significantly on the size of the firm? Explain your answer. Find a 95% confidence interval for the effect oflnFirmSize.

d) Test the overall significance of the model. (Follow the six steps of the test and do the hypothesis test at the1% level of significance.)

Question 3:

Use EViews for the following question. The file "Ass2Q3.xlsx"contains the data needed to answer the question. Make sure to include EViews output when it is used to answer the question.

The file "Ass2Q3.xlsx"contains data on demand for chicken from 1960 to 2011. Variable "Q" represents the annual quantity demanded for chicken,"P"its price and "I" shows the average level of income(for this question, assume that OLS conditions are satisfied).

a) Using these observations, estimate the demand function lnQ_i = α_o + α₁P_i^1/2 + α₁P_i^1/2 + ε_i. Report the results of the estimation.

b) Using the estimated regression from part (a) above, compute the estimated elasticity of demand with respect to price at the x-variable means (i.e.,P_m=$1 and I_m = $9.36)and interpret this estimate.

c) Re-estimate the demand function for chickenusing the lin-logmodel Q_i = β_o + β₁lnP_i + β₂lnI_i + ε_i and report the results.

d) Using the results from part (c), estimate the price elasticity of demand at P_m and I_m and interpret the estimate.

e) Estimate the log-logmodel lnQ_i = γ_o + γ₁lnP_i + γ₂lnI_i + ε_i, compute the estimated elasticity of demand and compare the results with those in parts (b) and (d).

f) Between thelog-logmodel andthe model in part (a), which one would you choose as thebetter model and why?

g) Use the estimated log-log model to test the hypothesis that demand is incomeinelastic.

Attachment:- Data.xlsx