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ECON 83A: STATISTICS FOR ECONOMIC ANALYSIS
MIDTERM #1 — FEBRUARY 12, 2020
MULTIPLE CHOICE QUESTIONS [18 PTS]
1. The entities on which data are collected are
a) elements.
b) populations.
c) samples.
d) observations.
2. For ease of data entry into a university database, 1 denotes that the student is an undergraduate and 2 indicates that the student is a graduate student. In this case data are
a) categorical.
b) quantitative.
c) either categorical or quantitative.
d) neither categorical nor quantitative.
3. Which of the following scales of measurement are appropriate for quantitative data?
a) Interval and ordinal
b) Ratio and ordinal
c) Nominal and ordinal
d) Interval and ratio
4. A survey of 800 college seniors resulted in the following crosstabulation regard- ing their undergraduate major and whether or not they plan to go to graduate school.
|
Graduate School |
Undergraduate Major |
Total |
||
|
Business |
Engineering |
Others |
||
|
Yes |
70 |
84 |
126 |
280 |
|
No |
182 |
208 |
130 |
520 |
|
Total |
252 |
292 |
256 |
800 |
The above crosstabulation shows
a) frequencies.
b) row percentages.
c) column percentages.
d) overall percentages.
5. The numbers of hours worked (per week) by 400 statistics students are shown below.
Number of hours Frequency
0–9 20
10–19 80
20–29 200
30–39 100
Total 400
The cumulative percent frequency for ≤ 29 hours is
a) 50.
b) 75.
c) 200.
d) 300.
6. Growth factors for the population of Atlanta in the past five years have been 1, 2, 3, 4, and 5. The geometric mean is
a) 15.
b) √15.
c) √120.
d) √5120.
7. The heights (in inches) of 25 individuals were recorded and the following statis- tics were calculated
mean = 70 range = 20
mode = 73 variance = 784
median = 74
The coefficient of variation equals
a) 11.2%.
b) 1120%.
c) 0.4%.
d) 40%.
8. Which difficulty of range as a measure of variability is overcome by interquartile range?
a) The sum of the range variances is zero.
b) The range is difficult to compute.
c) The range is influenced too much by extreme values.
d) The range is negative.
9. The sum of deviations of the individual data elements from their mean is
a) always greater than zero.
b) always less than zero.
c) sometimes greater than and sometimes less than zero, depending on the data elements.
d) always equal to zero.
10. The variance of the sample
a) can never be negative.
b) can be negative.
c) cannot be zero.
d) cannot be less than one.
11. A researcher has collected the following sample data.
5 12 6 8 5
6 7 5 12 4
The 75th percentile is
a) 7. b) 7.5. c) 8.
d) 9.
12. Which of the following descriptive statistics is not measured in the same units as the data?
a) 35th percentile
b) Standard deviation
c) Variance
d) Interquartile range
13. Each individual outcome of an experiment is called
a) the sample space.
b) a sample point.
c) a trial.
d) an event.
14. The intersection of two mutually exclusive events
a) can be any value between 0 to 1.
b) must always be equal to 1.
c) must always be equal to 0.
d) can be any positive value.
15. Of five letters (A,B,C,D,and E), two letters are to be selected at random. How many selections are possible?
a) 20 b) 7 c) 5! d) 10
16. An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is
a) 16. b) 8. c) 4. d) 2.
17. If A and B are independent events with P(A) = 0.35 and P(B) = 0.20, then,
P(A [ B) =
a) 0.07.
b) 0.62.
c) 0.55.
d) 0.48.
18. If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then
P(A j B) =
a) 0.209.
b) 0.000.
c) 0.550.
d) 0.380.
PROBLEM SOLVING QUESTIONS [42 PTS]
Problem 1. (12 pts) A private research organization studying families in various countries reported the following data for the amount of time 4-year-old children spent alone with their fathers each day.
Country Time with Dad (minutes)
Belgium 30
Canada 44
China 54
Finland 50
Germany 36
Nigeria 42
Sweden 46
United States 42
For the above sample, determine the following measures:
a) The mean (2 pts)
b) The variance (2 pts)
c) The standard deviation (1 pts)
d) The median (1 pts)
e) The mode (1 pts)
f) The 25th percentile (1 pts)
g) The 75th percentile (1 pts)
h) The range (1 pts)
i) The interquartile range (1 pts)
j) The coefficient of variation (1 pts)
Problem 2. (12 pts) Aubree, a college freshman, took 15 hours her first semester. Below is her grade report.
Class Credit Hours Grade
Physics 4 D
Biology 4 B
Statistics 3 B
Seminar 1 A
Macroeconomics 3 A
Aubree’s university uses a 4-point grading system, i.e., A = 4, B = 3, C = 2, D = 1, F = 0.
a) Compute Aubree’s grade point average at the end of the semester. (3 pts)
Aubree’s friend, Mike, took the same classes in his first semester. He received an A in Biology and Statistics, and a C in Physics, Seminar, and Macroeconomics.
b) Compute Mike’s grade point average at the end of the semester. (3 pts)
In the remaining calculations, use unweighted means whenever applicable. (As- sume the data represents a population.)
c) Compute and interpret the covariance of Aubree’sand Mike’s grades. (4 pts)
d) Compute and interpret the correlation coefficient. (2 pts)
Problem 3. (9 pts) On a recent holiday evening, a sample of 500 drivers was stopped by the police. Three hundred were under 30 years of age. A total of 250 were under the influence of alcohol. Of the drivers under 30 years of age, 200 were under the influence of alcohol.
Let A be the event that a driver is under the influence of alcohol. Let Y be the event that a driver is less than 30 years old.
a) Determine P(A) and P(Y). (2 pts)
b) What is the probability that a driver is under 30 and not under the influence of alcohol? (1 pts)
c) Given that a driver is not under 30, what is the probability that he/she is under the influence of alcohol? (1 pts)
d) What is the probability that a driver is under the influence of alcohol, when we know the driver is under 30? (1 pts)
e) Show the joint probability table. (2 pts)
f) Are A and Y mutually exclusive events? Explain. (1 pts)
g) Are A and Y independent events? Explain. (1 pts)
Problem 4. (9 pts) A machine is used in a production process. From past data, it is known that 97% of the time the machine is set up correctly. Furthermore, it is known that if the machine is set up correctly, it produces 95% acceptable (non- defective) items. However, when it is set up incorrectly, it produces only 40% acceptable items.
a) An item from the production line is selected. What is the probability that the selected item is non-defective? (3 pts)
b) Given that the selected item is non-defective, what is the probability that the machine is set up correctly? (3 pts)
c) Given that the selected item is non-defective, what is the probability that the machine is set up incorrectly? (3 pts)