Old Exam Questions for Practice Econ 29000 Kevin R Foster, CCNY |
|
|
with health insurance |
without health insurance |
female |
0.4905 (0.49994) N=7865 |
0.4811 (0.49990) N=950 |
Hispanic |
0.2587 (0.43797) N=7865 |
0.5411 (0.49857) N=950 |
African American |
0.1785 (0.38297) N=7865 |
0.1516 (0.35880) N=950 |
|
|
total |
|
A |
B |
C |
|
number in favor of candidate |
170 |
|
58 |
57 |
55 |
|
number total |
300 |
|
100 |
100 |
100 |
Note
that the standard deviation of the sample (not the standard error of the
average) is given.
a.
What is the probability, if the
true distribution has mean -1 and standard deviation of 1.5, of seeing a deviation
as large (in absolute value) as 2?
b.
What is the probability, if the
true distribution has mean 50 and standard deviation of 30, of seeing a
deviation as large (in absolute value) as 95?
c.
What is the probability, if the
true distribution has mean 0.5 and standard deviation of 0.3, of seeing a
deviation as large (in absolute value) as zero?
a.
What is the
probability, if the true distribution is a Standard Normal, if seeing a value
as large as 1.75?
b.
What is the
probability, if the true distribution is a Standard Normal, if seeing a value
as large as 2?
c.
If you observe a
value of 1.3, what is the probability of observing such an extreme value, if
the true distribution were Standard Normal ?
d.
If you observe a
value of 2.1, what is the probability of observing such an extreme value, if
the true distribution were Standard Normal ?
e.
What are the
bounds within which 80% of the probability mass of the Standard Normal lies?
f.
What are the
bounds within which 90% of the probability mass of the Standard Normal lies?
g.
What are the
bounds within which 95% of the probability mass of the Standard Normal lies?
a.
Find the area
under the standard normal pdf between -1.75 and 0.
b.
Find the area
under the standard normal pdf between 0 and 1.75.
c.
What is the
probability of finding a value as large (in absolute value) as 1.75 or larger,
if it truly has a standard normal distribution?
d.
What values form
a symmetric 90% confidence interval for the standard normal (where symmetric
means that the two tails have equal probability)? A 95% confidence interval?
a.
Find the area
under the normal pdf between 3 and 7.
b.
Find the area under
the normal pdf between 7 and 11.
c.
What is the
probability of finding a value as far away from the mean as 7 if it truly has a
normal distribution?
19.
A random variable is
distributed as a standard normal. (You
are encouraged to sketch the PDF in each case.)
a.
What is the probability that we
could observe a value as far or farther than 1.7?
b.
What is the probability that we
could observe a value nearer than 0.7?
c.
What is the probability that we
could observe a value as far or farther than 1.6?
d.
What is the probability that we
could observe a value nearer than 1.2?
e.
What value would leave 15% of
the probability in the left tail?
f.
What value would leave 10% of
the probability in the left tail?
20.
A random variable is
distributed with mean of 8 and standard deviation of 4. (You are encouraged to sketch the PDF in each
case.)
a.
What is the probability that we
could observe a value lower than 6?
b.
What is the probability that we
could observe a value higher than 12?
c.
What is the probability that
we'd observe a value between 6.5 and 7.5?
d.
What is the probability that
we'd observe a value between 5.5 and 6.5?
e.
What is the probability that
the standardized value lies between 0.5 and -0.5?
21.
You know that a random variable
has a normal distribution with standard deviation of 16. After 10 draws, the average is -12.
a.
What is the standard error of
the average estimate?
b.
If the true mean were -11, what
is the probability that we could observe a value between -10.5 and -11.5?
22.
You know that a random variable
has a normal distribution with standard deviation of 25. After 10 draws, the average is -10.
a.
What is the standard error of
the average estimate?
b.
If the true mean were -10, what
is the probability that we could observe a value between -10.5 and -9.5?
23.
You are consulting for a
polling organization. They want to know
how many people they need to sample, when predicting the results of the
gubernatorial election.
a.
If there were 100 people
polled, and the candidates each had 50% of the vote, what is the standard error
of the poll?
b.
If there were 200 people
polled?
c.
If there were 400 people
polled?
d.
If one candidate were ahead
with 60% of the vote, what is the standard error of the poll?
e.
They want the poll to be 95%
accurate within plus or minus 3 percentage points. How many people do they need to sample?
24.
Using the ATUS dataset that
we've been using in class, form a comparison of the mean amount of TV time
watched by two groups of people (you can define your own groups, based on any
of race, ethnicity, gender, age, education, income, or other of your
choice).
a.
What are the means for each
group? What is the average
difference?
b. What is the standard deviation of each mean? What is the standard error of each mean?
c.
What is a 95% confidence
interval for each mean?
d.
Is the difference statistically
significant?
25.
For
a Normal Distribution with mean -2 and
standard deviation of 3, what is the area to the right of 0.7?
26.
For
a Normal Distribution with mean -3 and
standard deviation of 3, what is the area to the left of 1.2?
27.
For
a Normal Distribution with mean -2 and
standard deviation of 9, what is the area to the right of -19.1?
28.
For
a Normal Distribution with mean -6 and
standard deviation of 4, what is the area to the left of -8.8?
29.
For
a Normal Distribution with mean 13 and
standard deviation of 4, what is the area to the left of 7?
30.
For
a Normal Distribution with mean -4 and
standard deviation of 1, what is the area to the right of -2.3?
31.
For
a Normal Distribution with mean -2 and
standard deviation of 9, what is the area to the right of -21.8?
32.
For
a Normal Distribution with mean 14 and
standard deviation of 0, what is the area to the left of 14?
33.
For
a Normal Distribution with mean 1 and
standard deviation of 6, what is the area to the right of -2?
34.
For
a Normal Distribution with mean 5 and
standard deviation of 9, what is the area to the left of -4?
35.
For
a Normal Distribution with mean 5 and
standard deviation of 8, what is the area to the left of 21?
36.
For
a Normal Distribution with mean 13 and
standard deviation of 2, what is the area to the right of 9.6?
37.
For
a Normal Distribution with mean -10 and
standard deviation of 5, what is the area in both tails farther from the mean
(in absolute value) than -7?
38.
For
a Normal Distribution with mean -1 and
standard deviation of 3, what is the area in both tails farther from the mean
(in absolute value) than -7?
39.
For
a Normal Distribution with mean 3 and
standard deviation of 3, what is the area in both tails farther from the mean
(in absolute value) than -4.2?
40.
For
a Normal Distribution with mean 0 and
standard deviation of 5, what is the area in both tails farther from the mean
(in absolute value) than -9.5?
41.
For
a Normal Distribution with mean 3 and
standard deviation of 9, what is the area in both tails farther from the mean
(in absolute value) than -0.6?
42.
For
a Normal Distribution with mean -7 and
standard deviation of 3, what is the area in both tails closer to the mean (in
absolute value) than -11.8?
43.
For
a Normal Distribution with mean -6 and
standard deviation of 8, what is the area in both tails closer to the mean (in
absolute value) than -5.2?
44.
For
a Normal Distribution with mean 4 and
standard deviation of 3, what is the area in both tails closer to the mean (in
absolute value) than -2.3?
45.
For
a Normal Distribution with mean -9 and
standard deviation of 6, what is the area in both tails closer to the mean (in
absolute value) than -7.2?
46.
For
a Normal Distribution with mean -4 and
standard deviation of 6, what is the area in both tails closer to the mean (in
absolute value) than 9.2?
47.
For
a Normal Distribution with mean -13 and
standard deviation of 5, what is the area in both tails closer to the mean (in
absolute value) than -20?
48.
For
a Normal Distribution with mean 9 and
standard deviation of 5, what is the area in both tails closer to the mean (in
absolute value) than 20?
49.
For
a Normal Distribution with mean -7 and
standard deviation of 2, what is the area in both tails closer to the mean (in
absolute value) than -10?