For questions 1 through 5, use the following data:
|
X
|
13
|
11
|
11
|
12
|
4
|
4
|
3
|
|
Y
|
8
|
13
|
12
|
8
|
9
|
10
|
2
|
1. What is the mean value of x?
2.What is the median value of x?
3. What is the sample variance of x?
4. What is the correlation coefficient between x and y?
5. What is the sample variance of the differences between x and y?
For questions 6 through 8, use the following contingency table:
|
A
|
not A
|
total
|
|
B
|
23
|
14
|
37
|
|
not B
|
36
|
30
|
66
|
|
total
|
59
|
44
|
103
|
6.Find the probability that B happens?
7. Find the probability that B happens given that A happens?
8. Find the probability that either A or B happens?
For questions 9 and 10, assume P(C)=0.2, P(D)=0.6, and P(C|D)=0.1.
9.Find the probability that C and D both happen?
10.Find the probability that D does not happen given that C happens. (Hint: Rewrite in terms of P(D|C) and apply Bayes theorem.)
11. Which of the following distributions are symmetric?
1.Select: F-distribution, Exponential distribution Normal distribution
2.Select: Binomial distribution, Poisson distribution, T-distribution
3. Select: Negative binomial distribution, Uniform distribution, Hypergeometric distribution
For questions 12 and 13, assume a loaded coin has a 70% chance of landing on heads each time it is flipped.
12. If you flip the loaded coin six times, what is the probability that it lands on heads exactly 3 times?
13. How much more likely is the loaded coin to land on heads 6 times than a fair coin would be? (That is, the difference in probabilities)
14. What is the probability that a normally distributed random variable takes a value that is larger than the value that is 2 standard deviations below its mean?
For questions 15 to 17, use the following distribution:
|
P(X)
|
0.1
|
0.35
|
0.2
|
0.3
|
0.05
|
|
X
|
1
|
2
|
3
|
4
|
5
|
15.What is the mean value of x?
16. What is the variance of x? (Hint: If you're using Excel, remember this is a population variance)
17. What is the probability that x is below its mean value?
18. If you estimate a regression model and find and intercept of 1 and a coefficient of 4, how should you interpret the coefficient of 4?
A:Y is four times as large as X.
B: On average, an observation with an x value one higher than another has a y value four higher than the other.
C: An increase in x causes y to increase by 4 times as much.
D: An increase in Y causes X to increase by 1/4 as much.
19 If you calculate a p-value of 0.01 for a hypothesis test, which of the following is the best interpretation?
A: There is a 1% chance that the null hypothesis is true.
B: If the null hypothesis were true, results this extreme would happen 1% of the time.
C: If the null hypothesis were false, results this extreme would happen 99% of the time.
D: There is a 99% chance that the null hypothesis is true.
For questions 20 through 22, suppose you draw a sample of size 120 from an unknown population and find a sample mean of 20 and a sample variance of 10.
20. What is the estimated standard error of the sample mean?
21.What is the upper bound of the 90% CI for the mean?
22.What is the test statistic for the null hypothesis that that the population mean is 0?
For questions 23 and 24, suppose you draw a sample of size 5 from a normal distribution and find a sample mean of 5.5 and a sample variance of 1.7.
23.What is the estimated standard error of the sample mean?
24.What is the lower bound of the 95% CI for the mean?
25.Suppose you have calculated a normally distributed test statistic with a value of 1.7. What is the corresponding p-value if you are using a two sided test?