Homework Problems Problem Sets Data Sets Spreadsheet Notes Notes Java Applets

# Econ 222: Introduction to Probability and Statistics II

Instructor: Tarık Kara
Office: MA-223
Phone: (290) 1458
E-mail: ktarik@bilkent.edu.tr

Lecture hours: Monday 15:40, 16:40 (A-127), Thursday 13:40, 14:40 (A-127).
Office hours: Tuesday 14:00-15:00, Wednesday 11:00-12:00

Assistant: Deniz Serdengeçti

Midterm dates:
1st Midterm: March 18, Tuesday
2nd Midterm: April 15, Tuesday

## Course Content:

This course is a continuation of ECON 221. We will cover the following topics: hypothesis testing, analysis of variance, goodness of fit, test for independence, correlation, simple linear regression, and multiple linear regression. Also, from probability theory we will cover joint and marginal distributions, conditional expectation and variance, independence of random variables, covariance and correlation of a pair of random variables.

## Textbooks:

P. Newbold, W.L. Carlson, and B. Throne, Statistics for Business Economics, Prentice Hall

## Software:

Several of the homework's will require the use of a computer. I would recommend the use of a spreadsheet program like EXCEL, OpenOffice, LibreOffice or Gnumeric. OpenOffice and LibreOffice are free office suites that include a spreadsheet program (Calc). The spreadsheet futures of Calc is not as strong as EXCEL but you ca n do most of the homework's with it. Gnumeric is a free spreadsheet program. The statistical functions of Gnumeric is better than EXCEL but lacks some other futures. You can download OpenOffice from http://www.openoffice.org/, LibreOffice from , and Gnumeric from http://projects.gnome.org/gnumeric/downloads.shtml.

## Course Outline:

• Hypothesis Testing
• Test for the population proportion (section 9.1, 9.4 and lecture notes).
• Test for the population mean (sections 9.2 and 9.3).
• Test for the difference between populations means (section 10.2).
• Test for the difference between populations proportions (section 10.3).
• Test for the population variance (section 9.6).
• Test for the ration of two population variances (section 10.4).
• Types of errors and power of a test (section 9.5 and material covered in lecture).
• Analysis of Variance:
• One-way analysis of variance (section 15.2).
• The Chi-Square Distribution and Analysis of Frequencies:
• Tests for goodness of fit (section 14.1 and 14.2).
• Tests for independence (section 14.3).
• Paired Data:
• Summarizing Descriptive Relations: Covariance and Correlation (section 2.4).
• Estimating the correlation coefficient and distribution of the sample correlation coefficient. Testing for correlation between two variables (section 11.7)
• Probability Theory: The case of several random variables: (sections 4.7 and 5.6)
• Joint and marginal distributions.
• Conditional distributions, conditional expectation, and conditional variance (not in the book).
• Independence of random variables.
• Covariance and correlation.
• Simple Linear Regression (chapter 11)
• Multiple Linear Regression (sections 12.1-12.6)
• Non-Parametric Tests (Chapter 15)
• Sign test.
• Wilcoxon Signed rank test.
• Mann-Witney test.

## Exercises, Quizzes, Exams, and Grading

Homework will be assigned almost every week and a random number of these homework's will be graded (homework's must be handed on time). Sometimes there will be a brief quiz during the lecture. There will be no makeup for missed homework's and quizzes.

There will be two midterms and a final exam. The material covered in all exams will be cumulative.

The course grade will be based on the following components, weighted as follows:

 Home works, quizzes and projects 10% 1st Midterm Exam (March 18, Tuesday) 25% 2nd Midterm Exam (April 15, Tuesday) 30% Final Exam 35%

I will try to grade according to the following grade descriptions prepared by the Faculty of Economics, Administrative, and Social Sciences:

A:
Outstanding performance during the course. The student meets all the standards stated in the course outline, expresses his/her ideas with full clarity, displays exceptional creativity and originality in dealing with the course-related tasks, is capable of taking initiative to carry out independent study regarding the course material and applying the skills and knowledge gained in the course to new situations and problems.
A-:
Excellent performance during the course. The student meets almost all the standards stated in the course outline, but has some minor flaws with regard to expression, creativity, independent study and/or application of the skills and knowledge gained in the course.
B+:
Very good performance during the course. The student meets most of the standards stated in the course outline, but has a few flaws with regard to expression, creativity, independent study and/or application of the skills and knowledge gained in the course.
B:
Good performance during the course. The student meets many of the standards stated in the course outline, but has one or two major flaws with regard to expression, creativity, independent study and/or application of the skills and knowledge gained in the course.
B-:
More than adequate performance during the course. The student meets more than the basic standards stated in the course outline, but also has some major flaws with regard to expression, creativity, independent study and/or application of the skills and knowledge gained in the course.
C+:
Acceptable performance during the course. The student meets barely more than the basic standards stated in the course outline, but also has several major flaws with regard to expression. The student displays some sign of creativity and independent study and requires some guidance for application of the skills and knowledge gained in the course to new situations.
C:
Acceptable performance during the course. The student meets only the basic standards stated in the course outline and has several major flaws with regard to expression. The student displays little sign of creativity and independent study, and requires much guidance for application of the skills and knowledge gained in the course to new situations. It is assumed that a student who receives the ``C'' grade (or above) should be able to proceed with other courses for which the given course is a prerequisite.
C-:
The student barely meets the basic standards stated in the course outline and has several serious flaws with regard to expression. The student displays very little sign of creativity and independent study, and requires considerable guidance for application of the skills and knowledge gained in the course to new situations.
D+:
The student has difficulty in meeting even the basic standards stated in the course outline and has many serious flaws with regard to expression. The student displays almost no sign of creativity, independent study and/or capacity for application of the skills and knowledge gained in the course to new situations.
D:
This is the lowest grade which will still enable a student to pass the course. The student meets only a few of the basic standards stated in the course outline and has numerous serious flaws with regard to expression. The student displays almost no sign of creativity, independent study and/or capacity for application of the skills and knowledge gained in the course to new situations. It is assumed that the student who receives a ``D'' grade can still proceed with other courses for which the given course is a prerequisite, but it is highly probable that s/he has to exert considerable effort to be successful in those courses.
FZ:
Failing: Not eligible to take the final exam: In this course every student will be eligible to take the final exam. Hence the FZ grade will not be given.
F:
Failing: Less than minimally acceptable performance. The student has taken the final exam but did not meet even the minimum standards stated in the course outline.
FX:
Failing: Less than minimally acceptable performance and did not take the final exam. The student did not take the final exam and did not meet even the minimum standards stated in the course outline.

## Course Objectives

A student completing this course should be able to:

• Given a claim about a population (about its mean, proportion, or variance):
1. State the appropriate null and alternative hypothesis. (D)
2. State the experiment to be used to test the hypotheses. (C)
3. Choose an appropriate test statistic to test the hypotheses. (D)
4. State the distribution of the test statistic. (D)
5. State the decision rule (D)
6. Find the critical values for the test statistic. (D)
7. Calculate the value of the test statistic for the sample obtained from the experiment. (D)
8. Decide to reject or fail to reject the null hypothesis and state the implications in plain English. (D)
9. Calculate the corresponding p-value. (C)
10. Calculate the probability of a Type I and Type II errors. (A)
• Given a claim about a pair of populations (about the difference between population means or proportions, or about the ratio between the population variances):
1. State the appropriate null and alternative hypothesis. (D)
2. State the experiment to be used to test the hypotheses. (C)
3. Choose an appropriate test statistic to test the hypotheses. (D)
4. State the distribution of the test statistic. (D)
5. State the decision rule (D)
6. Find the critical values for the test statistic. (D)
7. Calculate the value of the test statistic for the sample obtained from the experiment. (D)
8. Decide to reject or fail to reject the null hypothesis and state the implications in plain English. (D)
9. Calculate the corresponding p-value. (B)
10. Calculate the probability of a type I and type II error. (A)
• Given a claim which states that there is a difference between a set of populations:
1. State the appropriate null and alternative hypothesis. (D)
2. State the experiment to be used to test the hypotheses. (C)
3. Choose an appropriate test statistic to test the hypotheses. (D)
4. State the distribution of the test statistic. (C)
5. State the decision rule (D)
6. Find the critical values for the test statistic. (C)
7. Calculate the value of the test statistic for the sample obtained from the experiment. (C)
8. Decide to reject or fail to reject the null hypothesis and state the implications in plain English. (C)
9. Calculate the corresponding p-value. (B)
• For any claim about the distribution of a population:
1. State the appropriate null and alternative hypothesis. (C)
2. State the experiment to be used to test the hypotheses. (C)
3. Choose an appropriate test statistic to test the hypotheses. (C)
4. State the distribution of the test statistic. (C)
5. State the decision rule (C)
6. Find the critical values for the test statistic. (C)
7. Calculate the value of the test statistic for the sample obtained from the experiment. (B)
8. Decide to reject or fail to reject the null hypothesis and state the implications in plain English. (C)
9. Calculate the corresponding p-value. (C)
• Test if a given a data is generated by a random process:
1. State the appropriate null and alternative hypothesis. (C)
2. State the experiment to be used to test the hypotheses. (C)
3. Choose an appropriate test statistic to test the hypotheses. (C)
4. State the distribution of the test statistic. (B)
5. State the decision rule (C)
6. Find the critical values for the test statistic. (B)
7. Calculate the value of the test statistic for the sample obtained from the experiment. (C)
8. Decide to reject or fail to reject the null hypothesis and state the implications in plain English. (C)
9. Calculate the corresponding p-value. (C)
• Test a claim about a population (about its mean or median) when the assumptions of parametric tests are not satisfied:
1. State the null and alternative hypothesis. (B)
2. State the experiment to be used to test the hypotheses. (C)
3. Choose an appropriate test statistic to test the hypotheses. (A)
4. State the distribution of the test statistic. (A)
5. State the decision rule (B)
6. Find the critical values for the test statistic. (A)
7. Calculate the value of the test statistic for the sample obtained from the experiment. (B)
8. Decide to reject or fail to reject the null hypothesis and state the implications in plain English. (B)
9. Calculate the corresponding p-value. (A)
• Given any paired data:
1. Construct a table showing joint frequency distributions. (D)
2. Calculate the corresponding covariance and correlation. (D)
• Given a paired sample data from a population:
1. Estimate the population correlation coefficient (D)
2. Test if there is a correlation between the two quantities. (C)
• Given two random variables
1. Find the joint, marginal, and conditional distributions. (A)
2. Find the conditional expectation and conditional variance. (A)
3. Decide if two or more random variables are independent. (A)
4. Calculate the covariance and correlation between the two variables. (B)
• Given a simple (or multiple) linear regression model:
• Predict the value of one variable given the value(s) of the other(s). (B)
• Predict the expected value of one variable given the value(s) of the other(s). (B)
• Find a confidence interval for the value of one variable given the value(s) of the other(s). (B)
• State the distribution of the dependent random variable, given the value of independent variable(s). (A)
• State the distribution of the estimators for the intercept and the slope coefficients (A)
• Estimate the coefficients of a simple (multiple) linear regression model. (C)
• Determine if the regression model is significant. (C)
• Test a claim about a population (about its mean or median) when the assumptions of parametric tests are not satisfied:
1. State the null and alternative hypothesis. (B)
2. State the experiment to be used to test the hypotheses. (C)
3. Choose an appropriate test statistic to test the hypotheses. (A)
4. State the distribution of the test statistic. (A)
5. State the decision rule (B)
6. Find the critical values for the test statistic. (A)
7. Calculate the value of the test statistic for the sample obtained from the experiment. (B)
8. Decide to reject or fail to reject the null hypothesis and state the implications in plain English. (B)
9. Calculate the corresponding p-value. (A)
• Use EXCEL for all of the above. (C)
• Apply your knowledge to problems which are different than what we have done in class. (A)

## How to succeed in this (or any) course.

• Solve many questions.
• Attend lectures regularly.