251hwk 2/14/07 (Open this document in 'Outline' view!)
ECONOMICS 251 2005 COURSE OUTLINE WITH HOMEWORK ASSIGNMENTS
Most problems are exercises in the text. ‘text’ means Berenson et. al. – ‘*’ means that problem does not
appear or was not used in 8th edition. (8th edition numbers are in parentheses – ‘*’ means that problem does
not appear in 9th edition.) [9th edition numbers are in brackets – ‘!’ means that the problem does not appear
in earlier editions]
Downing and Clark (D&C) is the Barrons paperback. Problems that begin with letters are in the Syllabus
Supplement. (Numbers from 2002 – 2003 supplement are in parentheses) (Assignments may be changed
and solutions will be posted - check the website regularly )
A. Introduction
1. Definitions
Text exercise 1.12-1.14 [1.34 – 1.36] (1.31-1.33).
2. Uses of Statistics
B. Sources and Types of Data
1. Data
Text exercises 1.1-1.5, 1.9, 1.15, 1.16 [1.15-1.19, 1.23] (1.1 – 1.5, 1.9.)
2. Sources
3. Cross Section and Time Series Data
C. Presentation of Data
1. Classification
2. Tables
3. Charts and Graphs
D. Frequency Distributions and Populations.
1. Definitions
2. Graphs of the Frequency Distribution.
Exercises 2.22, 2.26, 2.1, 2.3[2.12, 2.13, 2.27, 2.34*], (2.12, 2.13, 2.25, 2.27*.)
Exercise 2.19
E. Sampling and Descriptive Statistics.
1. Sampling to Learn About a Population.
2. The Meaning of Random Sampling.
. Exercises 7.27, 7.28[1.10, 1.11] (1.21, 1.22)
3. Descriptive Statistics.
F. Measures of Central Tendency.
1. The Arithmetic Mean of Ungrouped Data.
2. The Arithmetic Mean of Grouped Data.
3. The Weighted Arithmetic Mean.
Problem F1 (In Syllabus Supplement)
4. The Median of Ungrouped Data..
5. The Median of Grouped Data.
6. The Mode
Exercises 3.1a, 3.2a (3.1a, 3.2a,) Downing and Clark pg 42 (pg 37 in 3rd ed) Problems 6,7(means, medians
and modes only).
7. Other Means.
Problem F2.
8. Measures of Position.
Downing & Clark, problem 7 above(Use data to find 1st decile, 99th percentile, 1st quintile, and 1st and 3rd
quartile), Problems F3, F4.
G. Measures of Dispersion and Asymmetry.
1. Range
Downing & Clark, problem 7 above (Use data to find IQR). Review solutions and terms on page 41 (36 in
3rd ed.) of Downing & Clark.
2. The Variance and Standard Deviation of Ungrouped Data.
Text exercises 3.1b, 3.2b, 3.6, 3.37, 3.24 [3.1b, 3.2b, 3.7, 3.37, 3.23] (3.1b, 3.2b, 3.7, 3.23, 3.33)
3. The Variance and Standard Deviation of Grouped Data.
Text exercises 3.28, 3.30 (3.68, 3.70) (work 3.30 in thousands), Downing & Clark pg 42 or 37, problems
6,7 (Find sample standard deviation – hint: run problem 6 in hundreds) (Note that you can use the Excel or
Minitab techniques in the graded assignment to compute and sum the fx and
and 7. ), Problems G1, G2. Graded Assignment 1
fx 2 columns in problems 6
4. Skewness and Kurtosis.
Find the standard deviation, coefficient of variation and measures of skewness in Text problem 3.1, 3.2.
Problems G3A, G4 (See 251wrksht).
5. Review
a. Grouped Data.
b. Ungrouped Data.
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H. Introduction to Probability
1. Experiments and Probability
Text problems 4.1, 4.2.
2. The Venn Diagram and the Addition Rule.
Downing & Clark, pg. 96 (pg 85 in 3rd ed) Basics 1, Application 2, 13. H1 (H0A), Text problems 4.3, 4.4,
4.10, 4.11, 4.8!, 4.9!.[4.3, 4.4, 4.8*, 4.9*]., (4.3,4.4, 4.8*, 4.9*)., H4, H5 (H1, H2).
3. Conditional and Joint Probability, Bayes’ Rule.
Text 4.16a-c, 4.18 [4.14a-c, 4.16] (4.13a-c, 4.15). H2, H3 (H0B, H0C), D&C pg 113 (pg 103 in 3rd ed) 14
(Note error in text - 5/6 of the people in the city support Jones, 5/9 of the people in the country support
Jones), 15, 16. H6 (H3).
4. Statistical Independence.
Text 4.16d, 4.22, 4.21!, 4.24, 4.30, 4.31, 4.33 [4.14d*, 4.19*, 4.20*, 4.22*, 4.28, 4.29, 4.31, 4.68*] (4.18*,
4.19*, 4.21*, 4.26, 4.27, 4.29). H8, H9 (H5, H6). pg. 97( pg. 85 in 3rd ed) Applications 4, 5, 8, 9, 10, 11,
44. H7(H4).
5. Review.
I. Permutations and Combinations.
1. Counting Rule for Outcomes.
Text 4.38, 4.41, 4.46 [4.36*, 4.39*, 4.43*]
2. Permutations.
4.47 [4.44*], D&C pg. 97( pg. 85 in 3rd ed) 19.
3. Combinations.
4.48 [4.45*], D&C pg. 97 20-21, 29-34. I1-I4.
J. Random Variables.
1. Definitions.
2. Probability Distribution of a Discrete Random Variable.
3. Expected Value (Expectation) of a Discrete Random Variable.
D&C pg. 140( pg. 97 in 3rd ed) means for 1 - 4. J1, J3. (J0A, J1)
4. Variance of a Discrete Random Variable.
D&C pg. 140 standard deviations for 1 - 4. J2 (J0B). Text 5.3, 5.4, 5.6. J4 –J7 (J2 – J5).
5. Summary
J8, J9 (J6, J7)
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6. Continuous Random Variables.
a. Normal Distribution (Overview).
b. The Continuous Uniform Distribution.
Text 6.23, 6.25 [6.24*, 6.26*], J10, J12 (J8. J10)
c. Cumulative Distributions, Means and Variances for Continuous Distributions.
d. Chebyschev's Inequality Again.
J11 (J9).
7. Skewness and Kurtosis (Short Summary).
K. Two Random Variables.
1. Regression (Summary).
2. Covariance (  xy and s xy )
3. The Correlation Coefficient (  xy and rxy )
4. Functions of Two Random Variables.
5. Sums of Random Variables, Independence.
In the following problems (i) check for independence, (ii) Compute Covx, y  , Corr x, y  and, (iii)
Compute Ex  y  and Var x  y  : D&C pg. 221 3, 4, 7, 14. In problem 3, find the following:


Px  y  4 , P x  y  4 x  0
Downing and Clark (formerly pg. 348 now posted at end of 251hwkadd) Old Computational Problem 1:
For the sample data below b) Compute Covx, y  and Corr x, y  . c) Compute the mean of x  y  and
Var x  y  .
x 34 26 9 30 47 10 34 34 45 10 47 37 47 8 45
y 6 57 89 60 95 42 31 28 90 25 45 23 52 95 48
Text 5.8 (Compute Var x  y  ), 5.9, 5.11, 5.16, 5.17 [5.8, 5.9, 5.10, 5.13] (5.8, 5.10), K1-K4 .
L. Discrete Distributions.
1. Binomial Distribution.
L1. Text 5.18-5.21, 5.23, 5.27[5.14a-d, 5.15, 5.16, 5.19, 5.20, 5.21] (5.15, 5.16, 5.18*, 5.19, 5.20).
2. Geometric Distribution.
L2-L5.
3. Poisson Distribution.
L6-L8. Text 5.30, 5.31, 5.33, 5.34, 5.35, 5.38[5.29 – 5.30, 5.34 - 5.37] (5.22 - 5.23, 5.26-5.29).
4. Hypergeometric Distribution.
Text 5.44-5.45, 5.49-5.50 [5.22 – 5.23, 5.27 – 5.28] (5.30, 5.31, 5.35, 5.36). L9, L10.
5. Review.
Note that problem L11 is a review of the continuous uniform distribution.
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M. Continuous Distributions.
1. Introduction.
These are optional! 6.28-6.32 [6.29 – 6.33] (6.24 - 6.28)
2. Properties of the Normal Distribution.
Text 6.1-6.2, 6.4!, 6.5a-c [6.1, 6.2, 6.5a-e.] (6.1, 6.2, 6.5a-e.) M1 a-g, M2, M3.
3. Percentiles and Intervals about the Mean.
Text 6.5d, 6.6!, 6.8 [6.4, 6.5f-h, 6.8.] (6.4, 6.5f-h, 6.8.) M4, M1 h-j. Graded assignment 4. M8.
4. Normal Approximation to the Binomial Distribution.
6.41 [6.57*], M6, M7.
5. Normal Approximation to the Poisson Distribution.
? [6.60*], M5.
Exercise 6.60(Not in 8th edition): The number of cars arriving per minute at a toll booth is Poisson
distributed with a mean of 2.5. What is the probability that in any given minute: a. No cars arrive.
b. Not more than 2 cars arrive? c. What is the approximate probability that in a ten minute period not more
than 20 cars arrive? d. What is the approximate probability that in a ten minute period between 20 and 30
cars arrive?
6. Review of Conditions for Approximation of One Distribution by Another.
N. Statistical Sampling.
1. Definitions.
2. Distribution of x and p
Text 7.11, 7.14 [7.12, 7.15] (7.12, 7.15)
3. The Central Limit Theorem
Text 7.1, 7.5, 7.67 on CD, 7.68, 7.71 [7.1, 7.5, 7.41, 7.42, 7.45] (7.1, 7.5, 7.40, 7.41, 7.44.) N1, N2.
O. Estimation of Parameters.
1. Point and Interval Estimation. Properties of Estimators.
2. A Confidence Interval for  When  is Known.
Text 8.1 -8.3, 8.8. (8.1 -8.3, 8.8.)
3. A Confidence Interval for  When  is not known.
Text 8.10, 8.11, 8.17, 8.21, 8.89! on CD [8.10, 8.11, 8.15, 8.20*]. (8.10, 8.11, 8.15, 8.17*). O1.
4. A Confidence Interval for a Proportion
Problem O2 (Black): a) A researcher wants to know what share her company holds in a large city. A sample
of 1003 people who bought CDs in the last month is taken and 256 turn out to have bought her company’s products
(CDs). Create a 95% confidence interval for the proportion that bought her company’s products. b) CD sales aren’t
what they used to be. What if we find out that there were only 10000 people who bought CDs in the city last month?
Addenda
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