计量经济学问题

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Question 2
(
3 marks
) At supermarkets the sales of canne
d tuna varies from week to week.
Marketing researchers have determined that th
ere is a relationship be
tween sales of canned
tuna and the price of
canned tuna. Specifically,
SALES = 40710 -430PRICE

(2),

where SALES are cans sold per week and PR
ICE is measured in cents per can. Suppose
PRICE over the year can be considered (appr
oximately) a normal random variable with mean
μ
=75 cents and standard deviation
σ
= 5 cents. That is PRICE ~ N(75,25).
i)   What is the numerical expected value of SALES? Show your work.
ii)  What is the numerical value of th
e variance of SALES? Show your work.  
iii) Find the probability that more
than 6300 cans are sold per week.  

Question 3
(
4 marks
) Suppose that a researcher, using wage data on 250 randomly selected
male workers and 280 female worker, estimates the simple model


Wage = 12.52 + 2.12Male,
R
2
= 0.06, SER=4.2
    (3),

          (0.23)     (0.36)
where Wage is measured in dollars per hour and Male
is a binary variable that is equal to 1 if
the person is a male and 0 if the person is
a female. Define the wage gender gap as the
difference in mean earnings
between men and woman.  

i)   Interpret the slope and the intercept in the model (3).
ii)  What is the estimated gender gap?  
iii) Write the (null) hypothesi
s testing for the gender gap.  
iv)  Another researcher uses these same data
but regresses Wages and Female, a variable that
is equal to 1 if the person is female and 0 if
the person is a male. What is the regression
estimates calculated from this
regression?  Show your work.  
                                      Wage =     ___  + ___Female      

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