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):
- State the appropriate null and alternative hypothesis.
(D)
- State the experiment to be used to test the hypotheses.
(C)
- Choose an appropriate test statistic to test the
hypotheses. (D)
- State the distribution of the test statistic. (D)
- State the decision rule (D)
- Find the critical values for the test statistic.
(D)
- Calculate the value of the test statistic for the
sample obtained from the experiment. (D)
- Decide to reject or fail to reject the null hypothesis
and state the implications in plain English. (D)
- Calculate the corresponding p-value. (C)
- 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):
- State the appropriate null and alternative hypothesis.
(D)
- State the experiment to be used to test the hypotheses.
(C)
- Choose an appropriate test statistic to test the
hypotheses. (D)
- State the distribution of the test statistic. (D)
- State the decision rule (D)
- Find the critical values for the test statistic.
(D)
- Calculate the value of the test statistic for the
sample obtained from the experiment. (D)
- Decide to reject or fail to reject the null hypothesis
and state the implications in plain English. (D)
- Calculate the corresponding p-value. (B)
- 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:
- State the appropriate null and alternative hypothesis.
(D)
- State the experiment to be used to test the hypotheses.
(C)
- Choose an appropriate test statistic to test the
hypotheses. (D)
- State the distribution of the test statistic. (C)
- State the decision rule (D)
- Find the critical values for the test statistic.
(C)
- Calculate the value of the test statistic for the
sample obtained from the experiment. (C)
- Decide to reject or fail to reject the null hypothesis
and state the implications in plain English. (C)
- Calculate the corresponding p-value. (B)
- For any claim about the distribution of a population:
- State the appropriate null and alternative hypothesis.
(C)
- State the experiment to be used to test the hypotheses.
(C)
- Choose an appropriate test statistic to test the
hypotheses. (C)
- State the distribution of the test statistic. (C)
- State the decision rule (C)
- Find the critical values for the test statistic.
(C)
- Calculate the value of the test statistic for the
sample obtained from the experiment. (B)
- Decide to reject or fail to reject the null hypothesis
and state the implications in plain English. (C)
- Calculate the corresponding p-value. (C)
- Test if a given a data is generated by a random process:
- State the appropriate null and alternative hypothesis.
(C)
- State the experiment to be used to test the hypotheses.
(C)
- Choose an appropriate test statistic to test the
hypotheses. (C)
- State the distribution of the test statistic. (B)
- State the decision rule (C)
- Find the critical values for the test statistic.
(B)
- Calculate the value of the test statistic for the
sample obtained from the experiment. (C)
- Decide to reject or fail to reject the null hypothesis
and state the implications in plain English. (C)
- 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:
- State the null and alternative hypothesis. (B)
- State the experiment to be used to test the hypotheses.
(C)
- Choose an appropriate test statistic to test the
hypotheses. (A)
- State the distribution of the test statistic. (A)
- State the decision rule (B)
- Find the critical values for the test statistic.
(A)
- Calculate the value of the test statistic for the
sample obtained from the experiment. (B)
- Decide to reject or fail to reject the null hypothesis
and state the implications in plain English. (B)
- Calculate the corresponding p-value. (A)
- Given any paired data:
- Construct a table showing joint frequency
distributions. (D)
- Calculate the corresponding covariance and correlation.
(D)
- Given a paired sample data from a population:
- Estimate the population correlation coefficient
(D)
- Test if there is a correlation between the two
quantities. (C)
- Given two random variables
- Find the joint, marginal, and conditional
distributions. (A)
- Find the conditional expectation and conditional
variance. (A)
- Decide if two or more random variables are independent.
(A)
- 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:
- State the null and alternative hypothesis. (B)
- State the experiment to be used to test the hypotheses. (C)
- Choose an appropriate test statistic to test the hypotheses. (A)
- State the distribution of the test statistic. (A)
- State the decision rule (B)
- Find the critical values for the test statistic. (A)
- Calculate the value of the test statistic for the sample obtained from the experiment. (B)
- Decide to reject or fail to reject the null hypothesis and state the implications in plain English. (B)
- 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.
- Ask questions.
- Use office hours.
- Stay on schedule.
- Work with others.