ECON 83A: STATISTICS FOR ECONOMIC ANALYSIS
MIDTERM #1 — OCTOBER 2, 2017
MULTIPLE CHOICE QUESTIONS [15 PTS ]
1. Data measured on a nominal scale
a) must be alphabetic.
b) can be either numeric or nonnumeric.
c) must be numeric.
d) must rank order the data.
2. The data measured on an ordinal scale exhibits all the properties of data mea- sured on
a) ratio scale.
b) interval scale.
c) nominal scale.
d) nominal and interval scales.
3. Given the following information: Standard deviation = 8
Coefficient of variation = 64% The mean would then be
a) 12.5. b) 8.
c) 0.64.
d) 1.25.
4. The standard deviation of a sample was reported to be 20. The report indicated that Σ (x - )2 = 7200. What is the sample size?
a) 16 b) 17 c) 18 d) 19
5. A researcher has collected the following sample data. The sample mean is 5. 3 5 12 3 2
The interquartile range is
a) 2.
b) 2.25. c) 6.
d) 9.
6. The variance can never be
a) zero.
b) larger than the standard deviation.
c) negative.
d) smaller than the standard deviation.
7. The geometric mean of 1, 2, 4, and 10 is
a) 2.99.
b) 4.25.
c) 17.0.
d) 4.0.
8. A six-sided die is tossed 3 times. The probability of observing three ones in a row is
a) 1/6.
b) 3/6.
c) 1/27.
d) 1/216.
9. There are twenty students in a class. How many different samples of three stu- dents can betaken from this population?
a) 1,140 b) 60
c) 6,840 d) 6
10. What is the number of permutations when we choose 4 objects from a set of 5?
a) 120 b) 30 c) 20 d) 5
11. The sum of the probabilities of two complementary events is a) 0.
b) 0.5.
c) 0.57.
d) 1.0.
12. In an experiment, events A and B are mutually exclusive. If P(A) = 0.6, then the probability of B
a) cannot be larger than 0.4.
b) can be any value greater than 0.6.
c) can be any value between 0 to 1.
d) cannot be determined with the information given.
13. If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then P(A [ B) =
a) 0.65.
b) 0.55.
c) 0.10.
d) 0.75.
14. If P(A) = 0.4, P(B j A) = 0.35, P(A [ B) = 0.69,then P(B) =
a) 0.14.
b) 0.43.
c) 0.75.
d) 0.59.
15. If P(A) = 0.3, P(B j A) = 0.1, P(A j B) = 0.75,then P(B) =
a) 0.0225.
b) 0.4444.
c) 0.0400.
d) 0.0444.
PROBLEM SOLVING QUESTIONS [45 PTS ]
Problem 1. (18 pts) In the period 1900–2016 there were thirty presidential elections in the United States. A sample of six elections was taken from this population. For each election data on the following variables were recorded: the name of the winner, their year of birth (YOB), their age when elected, and the number of states that they won. These data are reported below.
Election Winner YOB Age when elected States won
|
1920
|
Warren G. Harding
|
1865
|
55
|
37
|
|
1924
|
Calvin Coolidge
|
1872
|
52
|
35
|
|
1940
|
Franklin D. Roosevelt
|
1882
|
58
|
38
|
|
1944
|
Franklin D. Roosevelt
|
1882
|
62
|
36
|
|
1980
|
Ronald Reagan
|
1911
|
69
|
44
|
|
1992
|
William J. Clinton
|
1946
|
46
|
32
|
a) What measurement scale is used for each variable? Are these variables categor- ical or quantitative? (4 pts)
b) For age when elected, calculate the mean, the median, the 15-th percentile, and the 85-th percentile. (4 pts)
c) For age when elected and states won, calculate the range, the variance, and the standard deviation. (4 pts)
d) Compute and interpret the covariance for age when elected and states won. (3 pts)
e) Compute and interpret the correlation coefficient forage when elected and states won. (3 pts)
Problem 2. (9 pts) The flashlight batteries produced by one of the northern manu- facturers are known to have an average life of 60 hours with a standard deviation of 4 hours. Use Chebyshev’s theorem to answer the following questions.
a) At least what percentage of the batteries will have a life of 54 to 66 hours? (2 pts)
b) At least what percentage of the batteries will have a life of 52 to 68 hours? (2 pts)
c) Determine an interval for the lives of the batteries that will be true for at least 80% of the batteries. (4 pts)
d) Is it possible that 100% of the batteries will have a life determined by the interval in part c? (1 pts)
Problem 3. (8 pts) You are given the following information on events A,B, C & D.
P(A) = .4 P(A [ D) = .6
P(B) = .2 P(A j B) = .3
P(C) = .1 P(A ∩ C) = .04
P(A ∩ D) = .03
a) Compute P(D). (1 pts)
b) Compute P(A ∩ B). (1 pts)
c) Compute P(A j C). (1 pts)
d) Compute the probability of the complement of C. (1 pts)
e) Are A and B mutually exclusive? Explain your answer. (1 pts)
f) Are A and B independent? Explain your answer. (1 pts)
g) Are A and C mutually exclusive? Explain your answer. (1 pts)
h) Are A and C independent? Explain your answer. (1 pts)
Problem 4. (10 pts) A researcher studies the effectiveness of a new diagnostic test for Lyme disease. The results of her study suggest that 99% of infected individuals test positive. Individuals who are not infected have a probability of 4% of testing positive. It has also been determined that 1% of all patients are infected.
a) Find the probability of testing positive. (Round to 4 decimal places.) (4 pts)
b) Find the probability that an individual who tests positive is infected with Lyme disease. (3 pts)
c) Find the probability that an individual who tests positive is not infected with Lyme disease. (3 pts)