Nov. 1, 2001
ECON 240A-1
Midterm
L. Phillips
Answer all five questions
1. (15 points) All printed circuit boards (PCBs) that are manufactured at a certain plant
are inspected for flaws. Experience has shown that 50% of the PCBs produced are
flawed in some way. Of the flawed PCBs, 60% are repairable, while the remainder
are seriously flawed and must be discarded. A newly manufactured PCB is selected
before undergoing inspection. What is the probability that it will not have to be
discarded?
2. (15 points) Mensa is an organization where members possess IQ’s in the top 2% of
the population.
a. If IQ’s are normally distributed, with a mean of 100 and a standard deviation
of 16, what is the minimum IQ necessary for admission?
b. If three individuals are chosen at random from the general population, what is
the probability that all three satisfy the minimum requirement for admission to
Mensa?
3. (15 points) Determine the sample size needed to estimate a sample proportion with a
95 % confidence interval for its expected value of plus or minus 0.03, given
a. a sample proportion on the order of 0.05.
b. a sample proportion on the order of 0.5.
c. What distribution did you use in your calculations.
4. (15 points) The following graph 4-1 shows the results of regressing California
General Fund expenditures, in billions of nominal dollars, against California Personal
Income, in billions of nominal dollars beginning in fiscal year1968-69 and ending in
fiscal year 2001-02.
a. How much of the variance in the dependent variable is explained by personal
income?
b. Interpret the estimated slope.
Table 4-1 follows with the estimated parameters and table of analysis of variance.
c. Is the slope significantly different from zero? What statistic do you use to
answer this question? What distribution do you use to answer this question?
What probability were you willing to accept for a Type I error?
Nov. 1, 2001
ECON 240A-2
Midterm
L. Phillips
d. What is the ratio of the explained mean square to the unexplained mean square?
Calfifornia General Fund Expenditures Vs. California Personal Income, Billions of Nominal $
90
80
Gen Fund Expenditures
70
60
50
y = 0.066x - 1.1974
R2 = 0.981
40
30
20
10
0
0
200
400
600
800
1000
1200
1400
Personal Income
Figure 4-1: California General Fund Expenditures Versus California Personal Income,
both in Billions of Nominal Dollars
Table 4-1: Summary Output
Regression Statistics
Multiple R
0.9904673
R Square
0.9810255
Adjusted R Square
0.9804325
Standard Error
2.9988336
Observations
34
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
SS
1
32
33
MS
F
Significance
F
14878.68965 14878.69 1654.47398 3.98668E-29
287.7761003 8.993003
15166.46575
Coefficients Standard Error
t Stat
P-value
Lower 95% Upper 95%
-1.197411
0.927956018 -1.29037 0.20616709 -3.08759378 0.6927721
0.0659894
0.001622349 40.67523 3.9867E-29 0.062684796
0.069294
Nov. 1, 2001
ECON 240A-3
Midterm
L. Phillips
5. (15 points) The following graph 5-1 shows the results of regressing the logarithm of
California General Fund Expenditures (in billions of nominal dollars) against the
logarithm of California Personal Income (in billions of nominal dollars).
a. How much of the variance in the dependent variable is explained by the
independent variable?
b. Interpret the estimated slope.
c. Express the fitted equation in terms of the variables: California General Fund
Expenditures (fitted) and California Personal Income.
The Logarithm of California General Fund Expenditures Vs. The Logarithm of California
Personal Income, Billions of Nominal Dollars
CA Gen Fund Expenditures
100
1.0737
y = 0.0398x
2
R = 0.9877
10
1
10
100
1000
CA Personal Income
Figure 5-1: The Logarithm of California General Fund Expenditures Versus the
logarithm of California Personal Income, both in Billions of Nominal Dollars
Table 5-1 follows with the estimated parameters.
d. Test the hypothesis that the slope equals one.
e. What is the economic/political significance of this hypothesis test?
10000
Nov. 1, 2001
ECON 240A-4
Midterm
L. Phillips
Table 5-1:
Dependent Variable: LNGENFNX
Method: Least Squares
Sample: 1968 2001
Included observations: 34
Variable
Coefficient
Std. Error
t-Statistic
Prob.
LNPERSINC
C
1.073723
-3.224482
0.021175
0.125736
50.70825
-25.64487
0.0000
0.0000
R-squared
Adjusted R-squared
S.E. of regression
0.987708
0.987324
0.100384
Mean dependent var
S.D. dependent var
Akaike info criterion
3.091322
0.891602
-1.702610
Sum squared resid
Log likelihood
Durbin-Watson stat
0.322461
30.94437
0.347529
Schwarz criterion
F-statistic
Prob(F-statistic)
-1.612824
2571.327
0.000000
Figure5-2 follows.
Figure 5-2: Plot of Actual, Fitted and Residuals for the
Logarithm of California General Fund Expenditures
Regressed on the Logarithm of California Personal Income
5
4
3
0.3
0.2
2
0.1
1
0.0
-0.1
-0.2
70
75
80
Residual
85
90
Actual
95
00
Fitted
f. Is there any evidence of multicollinearity? Why or why not?
g. Is there any evidence of autocorrelation? Why or why not