# EC 370 Problem Set 1 (2015)

September 29, 2018

Use the following information to answer question1-4.
Reviewing her performance on her last ten (10) three foot
putts, Lisa see the following pattern:

Make, Make, Miss, Make, Miss, Make, Make, Make, Miss

1.
Enter a one?1?for every make and zero (0) for every
miss. What is the mean of this sample of putts?
a.
3/5
b.
b. 7/10
c.
c. 3/2
d.
d. 1/2
e.
e. 3/1

2.
What is the conditional probability of a make on
a put following a miss?
a.
2/3
b.
1/10
c.
1/2
d.
1/5
e.
4/5

3.
What is the conditional probability that Lisa
a.
0
b.
1/3
c.
2/5
d.
1
e.
2/3

4.
How many runs are there?
a.
3
b.
5
c.
6
d.
10
e.
4

Frustrated with her performance. Lisa practices 100 putts. She calculates 42
runs. The W-W runs test gives the following information.
Expected number of Runs:49; sd; 4.7737; z-score=-1.4664

5.
At the 5% level of significance, which of the
following is true?
a.
The number of runs is not significantly
different from the expected number of runs.
b.
The number of runs is significantly less than
the expected number of runs.
c.
The number of runs is not significantly
different from zero
d.
The number of runs is significantly less than
zero
e.
The number of runs is significantly greater than
the expected umber of runs.

6.
Does the data provide evidence that Lisa has a
hot hand?
a.
Yes, because the number of runs is significantly
less than the expected number of runs.
b.
Yes, because the number of runs is significantly
greater than the expected number of runs.
c.
No, because the number of runs is significantly
less than the expected number of runs.
d.
No, because the number of runs is significantly
greater than the expected number of runs.
e.
No, because the number of runs is not
significantly different than the expected number of runs.

7.
The z-score means that the number of runs is
roughly
a.
1.4664 standard deviations below the expected
number of runs.
b.
About 1.47% percent likely to be significantly
different from the expected number of runs.
c.
1.4664 more than the expected number of runs.
d.
1.4664 standard deviations above the expected
number of runs.
e.
1.4664 less than the expected number of runs.

Lisa is also worried about her
consistency on the golf course. She thinks that she has “ post-birdie syndrome”.
This condition shows up on the hole following a birdie (one under par on a golf
hole). She thinks that she becomes overconfident and score worse ( remeber that
in golf, a higher score is worse!) Like a good economist, she has gathered data
to test her theory.

Score par or below Score above par

(success) ( failure)
Hole following a birdie 11 22

Hole not following a birdie 62 54

8.
What test should she perform to determine
whether she has post-birdie syndrome?
a.
Multiple Regression
b.
Standard Deviation test
c.
Runs test
d.
Single regression
e.
Chi Square test

9.
Which best describes the hypothesis that she is
testing ( the alternative hypothesis, Not the null hypothesis)?
a.
“ On average, I score lower ( I get a better
score) after a birdie than I do otherwise”
b.
“I have a hot hand”
c.
“I do not have a hot hand”
d.
“On average, I score higher( I get a worse
score) after birdie than I do otherwise”
e.
“On average, I score the same after a birdie as
I do otherwise”

Lisa runs the appropriate
test, which returns a p-value of 0.032

10. What
does this p-value mean?
a.
If the null hypothesis is true, then Lisa’s
probability of making a type II error is 96.8%(0.968)
b.
If the null hypothesis is correct, the
probability of observing this much or more difference between scores is
3.2%(0.032)
c.
The correlation coefficient for her scores is
0.032.
d.
Her score after a birdie is 3.2% higher than her
score before a birdie.
e.
If the null hypothesis is true, then Lisa’s
probability of making a type II error is 3.2% (0.032)

11. Suppose
that Lisa had decided on a 5% significance level. Does she conclude that she
has post-birdie syndrome?
a.
Yes, because she scores lower after a birdie.
b.
Impossible to tell, because we do not have the
Z-statistic.
c.
Yes, because her p-value is less than 5%
d.
No, because her p-value is less than5%
e.
No, because her p-value is less than the 5%
critical value of 1.96.

12. Suppose
that we divided her scores into groups of five, if we plotted the frequency
distribution of number of scores in each group of five that were above par, we
would plot a
a.
Binomial distribution
b.
Geometric distribution
c.
Student’s t-distribution
d.
Normal distribution
e.
Chi square distribution

Height is measured in inches, BMI is body Mass index (weight in kilograms
divided by height in meters squared). Wonderlic is the score on an intelligence
test, 40 yard dash is measured in seconds and Division I-AA dummy answers the
question, “ was your college in division I-AA? (1 for yes and 0 for a no)

13. What
is the dependent variable?
a.
Constant
b.
Draft position
c.
Division I-AA dummy
d.
Height

14. Is
the coefficient on Height statistically different from zero at the 5%
significance level?
a.
Yes, because the coefficient is more than1.96%
times as large as the standard error in absolute value.
b.
Yes, because the p-value is smaller than the coefficient.
c.
No, because its standard error is very large in
absolute value (higher than any other standard error.
d.
Yes, because neither the coefficient nor the
standard error equals zero.
e.
No, because the standard error is negative.

15. What
is the t0statistic for testing whether the coefficient on Height is different
from zero?
a.
(-19.55)*(-4.24)
b.
-19.55
c.
(-19.55)/(-4.24)
d.
(-19.55)/(-4.24)
e.
-4.24

16. After
controlling for all other independent variables in the regression, what is the
effect of Height on draft position?
a.
A one inch increase in height leads to an
increase in draft position ( Later in the draft) of 19.55 spots.
b.
A one inch increase in height leads to a
decrease in draft position ( earlier in the draft) of 19.55 spots.
c.
A one inch increase in height leads to an
increase in draft position ( later in the draft) of 4.24 spots.
d.
A one inch increase in height leads to a
decrease in draft position ( earlier in the draft) of 4.25 spots.
e.
There is no statistical relationship between
height and draft position at the 5% significance level.

17. Consider
two divisions I-AA quarterbacks with the same height, BMI, and Wonderlic score.
One has a 40 yard dash of 4.5 seconds, while the other has a 40 yard dash of
5.5 seconds. The model predicts that the FASTER quarterback with roughly
a.
129 positions earlier.
b.
129 positions later.
c.
3 positions earlier.
d.
3 positions later
e.
There is no statistical relationship between 40
yard dash and draft position at the 5% significance level.

18. The
95% confidence interval for the estimate of the effect on draft position of
playing at a Division I-AA college is about
a.
0 to 55.96
b.
49.47 to 62.45
c.
52.65 to 59.27
d.
16.91 to 185.23
e.
3.31 to 55.96

In a recent paper “Catching a Draft: on the process of selecting
quarterbacks in the NFL draft, “ Berri and Simmons try to explain the draft
position of quarterbacks, which is a number from1 (1st pick in the 1
st round) ro250 (last pick in the last round). They present the following
regression table.

Variable I
Constant 4963.03
3.04
Height -19.55
-4.24
BMI -272.67
-2.42
BMI squared 4.68
2.33
Wonderlic -1.94
-1.82
40 yard dash 128.81
3.16
Division I-AA dummy 55.96
3.31

19. After
controlling for height, Wonderlic score, 40 yard dash time, and Division I-AA
status, does the model predict that players with higher BMI will always be
drafter later than players with lower BMI?
a.
true
b.
false

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