Download Economics 310: Economic Statistics Quick Review for Exam 1, part b

Economics 310: Economic Statistics
Quick Review for Exam 1, part b
Exam 1, part b covers chapter 2, 3 and class notes.
Complete the following exercises for a cursory review of the concepts that you will be tested
upon on this exam. These questions are not a substitute for the assigned homework nor
should they be construed as a study guide!
Merely stating answers to calculations is insufficient to receive complete credit. Calculators
may be used to aid in your calculations but formulas and set up of mathematical problem
must be shown to receive full credit. Finally, one 8 ½” X 11” sheet of paper may be used as a
formula card with any formulas or notes that you wish to write on both sides.
1. True or false: the average (mean) age of people who respond to a particular survey is an
example of a parameter.
2. The first two classes of a frequency distribution are 0 – 9 and 10 – 19. What is the class
length?
3. The first two classes of a frequency distribution are 0 – 9 and 10 – 19. What are the class
boundaries of the first class?
4. Can the original 27 values of a data set be identified by knowing that 27 is the frequency
for the class 0 – 9? Why or why not?
5. True or false: When a die is rolled 600 times, each of the 6 possible outcomes occurs
about 100 times as we normally expect, so the frequency distribution summarizing the
results is an example of a normal distribution. Explain and elaborate your answer.
6. Fill in the blank: For typical data sets, it is important to investigate center, types of
distribution, ___________ and outliers.
7. What values are represented by this stem and leaf diagram? 5 | 2 2 9
8. Which graph is best for paired data consisting of shoe sizes and heights of 30 randomly
selected students: histogram, dotplot, scatterplot, pie chart? Explain and elaborate your
answer.
9. True or false: A histogram and a relative frequency histogram constructed from the same
data always have the same basic shape, but the vertical scales are different.
10. What characteristic of a data set can be better understood by constructing a histogram?
Professor Camarena
Bowerman Text, 4th edition
11. Construct a dotplot of the pulse rates of males listed in the following table.
68
72
56
88
64
56
64
56
88
68
60
64
72
64
64
56
64
60
84
56
72
68
76
60
60
60
84
64
88
60
88
72
76
56
96
72
60
84
72
84
12. When we compute the sample mean and standard deviation for the pulse rates of males
we find that x is 69.4 and s=11.29738. Compute each of the intervals [x ± s], [x ± 2s], [x
± 3s]. Then count the number of pulse rates that actually fall into each interval and find
the percentage of pulse rates that fall into each interval.
13. How do the percentages of the pulse rates that fall into the intervals [x ± s], [x ± 2s], [x ±
3s] compare to those given by the Empirical Rule? How do the percentages of the pulse
rates that fall into the intervals [x ± 2s] and [x ± 3s] compare to those given by
Chebyshev’s Theorem?
14. What is the mean of the sample values 2 cm., 2 cm., 3 cm., 5 cm, and 8 cm.?
15. What is the median of the sample values listed in question 14?
16. What is the mode of the sample values listed in question 14?
17. If the standard deviation of a data set is 5.0 feet, what is the variance of the data set?
18. If a data set has a mean of 10.0 seconds and a standard deviation of 2.0 seconds, what is
the z score corresponding to the time of 4.0 seconds?
19. Fill in the blank: The range, standard deviation, and variance are all measures of
________ for a data set.
20. What is the symbol used to denote the standard deviation of a sample, and what is the
symbol used to denote the standard deviation of a population?
21. What is the symbol used to denote the mean of a sample and what is the symbol used to
denote the mean of a population?
22. Fill in the blank: Approximately ____ percent of values in a sample are greater than or
equal to the 25th percentile.
23. True or false: For any data set, the median is always equal to the 50th percentile.
Professor Camarena
Bowerman Text, 4th edition
Economics 310: Economic Statistics
Quick Review for Exam 1, part b
Answer Key
1.
False. The mean age of people who respond to a survey is a sample statistic. Survey data
cannot yield population parameters.
2. Ten as each of the numbers of the class boundaries are included in the class. As such, there
are ten numbers between 0 and 9.
3. 0.5 and 9.5
4. Yes. Knowing that the first class of the table has a frequency equal to 27 indicates that all of
the data values in the data set have been accounted for. The true question then becomes, why
did all of the data values fall into the first class? Additional analysis must be done to
determine if the class width is appropriate given the data set.
5. False. A normal distribution is characterized by
frequencies that start low, peak in the middle, and end
low. A symmetric or bell shaped curve can be expected.
In this scenario, a uniform distribution is obtained. A
uniform distribution occurs when each class’ frequency
is identical. A histogram with a uniform distribution
looks like this.
6. Changes in patterns of data over time, dispersion, or any other answer you can think of that
accurately finishes this statement.
7. 52, 52, 59
8. Scatterplot. A scatterplot shows the relationship between two variables. All of the other
graphs listed as answer choices are limited to showing data from only one variable.
9. True
10. The underlying distribution of the data set. A histogram is used to construct the underlying
“curve” that the data fall in. The dispersion of the data as well as outliers can also be
identified with a histogram. A histogram is also a good gauge for the data set’s place of
center.
Professor Camarena
Bowerman Text, 4th edition
11.
12.
Percen
Number of
t of
observations Total
1
standard
deviation
2
standard
deviations
3
standard
deviations
58.10262
to
80.69738
25
62.50%
46.80524
to
91.99476
39
97.50%
to
103.2921
4
40
100%
35.50786
13. The
empirical rule states that approximately 68% of all observations will fall within one standard
deviation; 95% of all observations will fall within two standard deviations and 100% of all
data observations will fall within three standard deviations.
Chebyshev’s theorem states that at least (1-1/z2) of the data values must fall within z standard
deviations of the mean, where z is any value greater than 1. Chebyshev’s Theorem cannot
predict percentages of data within one standard deviation. Chevyshev’s Theorem does
predict that at least 75% of the data must be within two standard deviations of the mean, 80%
of the data must lie within three standard deviations of the mean, and 94% of the data must
lie within four standard deviations from the mean.
Comparing these two rules to the actual data observed, it can be seen that distribution of the
pulse rates of males most closely resembles the expectations outlined by the empirical rule.
14. 4 cm.
15. 3 cm.
16. 2 cm.
17. Variance = 25.0 feet
18. Z = -3.00
19. Dispersion
20. Sample = s, population = σ
21. Sample = x , population = μ
22. 75%
23. True
Professor Camarena
Bowerman Text, 4th edition