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 made the putt given that she made the two previous putts?
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
syndromeâ€. 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 otherwiseâ€
b.
“I have a hot handâ€
c.
“I do not have a hot handâ€
d.
“On average, I score higher( I
get a worse score) after birdie than I do otherwiseâ€
e.
“On average, I score the same
after a birdie as I do otherwiseâ€
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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