-----------------------------------------------------------------------
               Econ 120B, Winter 1998  --  Homework #2 (5%)
-----------------------------------------------------------------------
This homework is due at 2:20pm on Tuesday, February 24, 1998.  Papers
turned in at the end of the class will carry a 10% penalty and those
turned in later than that will carry a 25% penalty PER DAY.  As before,
team up with others (maximum 3 persons per team) and submit a single 
paper with all names.

First of all, carry out the Practice Computer Session posted on the 
internet using the ESL/ESLWIN programs.  This will give you practice
for the following exercise.

I.
Consider the following two models of the expenditures for maintenance 
of a certain automobile.  For simplicity, the t subscript is ignored.

     cost  =  a1 + a2 miles + u
     cost  =  b1 + b2 age + v

where cost is the cumulative expenditure on maintenance (excluding
gasoline), in dollars, miles is the number of miles driven in
thousands, and age is age of the car in weeks.  The file data3-7 has
time series data with 57 observations.  Use ESL/ESLWIN to estimate the
above models by following the steps given below.

Double click the ESLWIN icon, select Estimate, Interactive, Text-book 
data set, and choose data3-7.  ESL will read the data and stop at the 
prompt ?.  To estimate the two models, the commands are
     ols  cost  0  miles  ;
     ols  cost  0  age  ;
0 is the number zero which stands for the intercept term.  Type quit
to exit ESLWIN.  Follow screen directions and obtain the printout.
This is to be attached with the answers to the following questions.  
ONLY THE ORIGINAL PRINTOUT WILL BE ACCEPTED, NO XEROX COPY.  But keep a
Xerox copy for yourself to study for the exam.

1.  What signs do you expect for a1, a2, b1, and b2? Explain why.  Do
    the actual signs agree with your intuition?
2.  What is the economic interpretation of a2 and b2?
3.  Which of the models do you think is "better"?  Clearly state what
    criteria you choose to determine which is better.
4.  Test each model for overall goodness of fit at the 1 percent level.
5.  In the two models, SEPARATELY test the null hypotheses, a1 = 0,
    a2 = 0, b1 = 0, and b2 = 0, against a two-side alternative in each 
    case.  Be sure to use both the t-table approach and the p-value 
    approach (choose a 1 percent level of significance).
6.  In the second model, suppose age is measured in days rather than 
    weeks.  Write down the new estimates of the model in the form 
    presented in Page 113 of the book (Page 112 in the third edition).

II.
A manufacture of tires knows from past experience that the average life 
of a particular model follows the normal distribution.  He believes that 
the average life of a tire is 30,000 miles.  He hires you to test
whether or not that is the case.  You draw a random sample of 121 tires
and measure the life of each one.  You find the sample average life to
be 31,200 with a standard deviation of 625.

1.  State the null and alternative hypotheses for this.
2.  Calculate the test statistic and state its distribution under the
    null and the d.f.
3.  State the criteria for rejection or acceptance of the null and apply
    it at the 5 percent level of significance.  What is your conclusion?
4.  Derive the 95 percent confidence interval for the average life.