Download WIDENER UNIVERSITY

WIDENER UNIVERSITY
SCHOOL OF BUSINESS ADMINISTRATION
Fundamental Statistics for Business & Economics (QA501)
Professor Karen Leppel
E-mail: [email protected]
Office hrs: MWF: 1:00 - 2:30 p.m.; Th: 5:45-6:15 p.m.
Syllabus - Spring 2002
Office: 526 E. 14th St.- 3rd floor
Office Telephone: (610) 499-1170
-----------------------------------------------------------------------------PREREQUISITES: QA500 (Mathematical Analysis: Algebra and Calculus).
COURSE OBJECTIVE: This course is designed to introduce students to probability and
statistics and provide students with the basic statistical tools for decision-making.
LEARNING OBJECTIVES: At the completion of this course, the student should be able to:
(1) Graph a frequency distribution;
(2) Compute summary statistics of measures of central tendency and the spread of a
distribution;
(3) Use the rules of probability to determine the probabilities of different events occurring;
(4) Determine whether the uniform, binomial, multinomial, hypergeometric, or Poisson
distribution is appropriate in a particular context;
(5) Calculate the mean and variance of a random variable, and the covariance and correlation
coefficient of a pair of jointly distributed variables;
(6) Distinguish between the concepts of systematic error and random error;
(7) Use the standard normal and t distributions to calculate probabilities;
(8) Calculate confidence intervals for the population mean, the difference between two
population means, the population proportion, and the difference between population
proportions;
(9) Perform hypothesis testing on population means, comparisons of population means,
population proportions, and comparisons of population proportions;
(10) Perform chi-square tests to determine the goodness of fit of a theoretical distribution to an
observed distribution; perform a chi-square test to determine whether two variables are
independent of each other.
(11) Perform one-factor and two-factor analysis of variance.
TEXTBOOK & SOFTWARE:
(1) Business Statistics: A First Course, 2nd ed., by D.M. Levine, T.C. Krehbiel & M.L. Berenson.
(2) Adventure Learning Systems: Statistics (Software Package).
COURSE POLICY:
Computer software: The software provides problem-solving practice and gives
immediate feedback on responses. The software may be used in either practice mode or
certification mode. Certification mode counts the number of errors made in a particular module.
If the student completes the module with less than a specified number of mistakes, the computer
provides the student with a certification code for that module. The student then goes to the
Widener computer network and registers the certification code, which the instructor can access.
Important Note: To use the software, each student must have an access code. To get
your code, you must purchase the "Adventure Learning Systems: Statistics" software. Then go
to www.quantsystems.com, click on Authorization Codes at the bottom of the web page, enter
the coupon information you received when you purchased the software. If you have a problem
getting your code, call Quant Systems at 800-426-9538.
Written homework problems: To provide practice on problems not available in the
software package, additional homework problems are assigned. Some are “Textbook Problems”
and some are “Syllabus Problems.”
Exams: There will be two exams and a final exam. The two exams will be given after
syllabus sections IV and VII. The final exam covers the material from the entire course.
Depending on the performance of the class, exam grades may be curved. Adjusted grades will
be determined based on students' relative positions in the appropriate grade ranges. (For
example, a middle B will be adjusted to equal an 85.) Plus and minus grades will not be given
for final course grades. Make up exams will not be given without a written excuse from a
physician or other appropriate authority.
Course Grade: Students may choose to have their final course grade determined in one
of two ways. In option 1, the student does not need to earn the computer certificates. (The
student just does as much practice on the computer as the student feels he/she needs.) The
course grade is determined solely on the basis of the exams. The two hourly exams count 30%
each and the final counts 40%. In option 2, the student completes and registers the twenty-one
assigned “certificates.” If the student completes, for example, 80% of the certificates, the
certificate portion of the grade is an 80. Then the certificate grade counts as 20% of the final
course grade, each of the hourly exams counts 25%, and the final exam counts 30%.
Summary of course grade determination:
2 exams
final exam
computer software certificates
option 1
60%
40%
0%
---100%
option 2
50%
30%
20%
---100%
SKILLS OUTCOMES:
(1) Quantitative Skills:
(a) Skills-In: Background in Algebra.
(b) Skills-Out: Ability to compute descriptive statistics, calculate probabilities, determine point
estimates and confidence intervals, and perform hypothesis tests and analysis of variance.
(2) Computer Skills:
(a) Skills-In: Basic knowledge of the computer keyboard.
(b) Skills-Out: (i) Ability to apply Excel to perform statistical calculations.
(ii) Ability to use the computer to answer questions concerning probability and statistics.
TEACHING TECHNIQUES: lectures, problem solving, computer software problems
COURSE OUTLINE:
I. Appendix A: Review of Arithmetic and Algebra, & Appendix B: Summation Notation.
(Students are expected to read these appendices on their own. Students having questions on this
material should contact the instructor or seek help from the Math Center.)
II.
Chapter 1: Introduction and Data Collection
Topics:
Populations and Samples
Parameters and Statistics
Control Group
Systematic Error or Bias (including measurement error)
Random Error or Sampling Error (due to chance factors)
Sampling with and without replacement
III. Chapters 2 and 3: Presenting and Describing Data (excluding section 3.3)
Topics:
Frequency Distributions: absolute & relative frequencies, cumulative frequencies
Summary Measures: center of distribution (mean, median, mode), dispersion (range, mean
absolute deviation, mean squared deviation, variance, standard deviation, coefficient of
variation)
Problems and Certificates:
1. Certificate – "Descriptive Statistics" (Lesson 2.2)
2. Syllabus Problem – A
IV. Chapter 4 (sections 4.1 to 4.3) – Introduction to Probability
Topics:
Definitions: sample space, event, objective probability
Counting: multiplication rule, permutations, combinations
Joint Probability & Marginal Probability
Conditional Probability and Bayes rule
Independent Events and Mutually Exclusive Events
Birthday Problem
Problems and Certificates:
1. Textbook problems: p. 174: 4.21; p. 178: 4.29, 4.31
2. Syllabus problems – B, C, D
V. Chapter 4 (sections 4.4 to 4.6) – Discrete Random Variables
Topics:
Definition of discrete random variable
Expected value & variance of discrete random variables
Mean and Variance of standardized random variable
Expectation Rules
Jointly Distributed Random Variables
Independent Random Variables
Covariance and Correlation Coefficient
Specific Discrete Random Variable Distributions: uniform, binomial, multinomial,
hypergeometric, Poisson
Problems and Certificates:
1. Certificates
"Discrete Random Variables" (Lesson 3.7)
"Binomial Word Problems” (Lesson 3.5)
"Hypergeometric Word Problems" (Lesson 3.8)
"Poisson Word Problems" (Lesson 3.6)
2. Textbook problems: p. 193: 4.42 - also determine the mean and standard deviation of X/n.
3. Syllabus problems – E, F, G
VI. Chapter 4 (sections 4.7 – 4.9) & Chapter 5 (section 5.1):
Continuous Distributions & Sampling Distributions
Topics:
Continuous Distributions
Normal and t Distributions
Normal Approximation of Binomial and Continuity Correction
Central Limit Theorem and Distribution of the Sample Mean
Finite Population Correction Factor
Problems and Certificates:
1. Certificates
"The Standard Normal" (Lesson 4.1)
"Normal Probability Word Problems" (Lesson 4.2)
"Find the Value of Z" (Lesson 4.3)
"Find the Value of t" (Lesson 4.4)
"Sampling Distributions (Means)" (Lesson 5.2)
"Sampling Distributions (Proportions)" (Lesson 5.3)
2. Syllabus problem – H
VII. Chapter 5: Estimation (sections 5.2- 5.6)
Topics:
Estimators, Point Estimates and Interval Estimates
Properties of Good Estimators: unbiasedness, efficiency, sufficiency, and consistency
Confidence Intervals for Population Mean: known variance & unknown variance
Confidence Interval for Population Proportion
Confidence Interval for the Difference between Population Means: variances known, variances
unknown, variances unknown but believed equal
Confidence Interval for the Difference between Population Proportions
Determining appropriate sample size
Problems and Certificates:
1. Certificates
"Estimation (Means)" (Lesson 6.1)
"Estimation (Means)" – Small Samples (Lesson 6.2)
"Estimation (Proportions)" (Lesson 6.3)
2. Syllabus problems – I, J
VIII. Hypothesis Testing on Means and Proportions
Textbook Reading: Chapter 6, Chapter 7 (sections 7.1 and 7.3), and Chapter 8 (section 8.1)
Topics:
null and alternative hypotheses
type I and type II errors
critical and acceptance regions
one- and two-tailed tests
p-values
tests for population mean: known population variance, unknown population variance
test for population proportion
tests for the difference between population means for independent samples: population
variances known, population variances unknown, population variances unknown but
believed equal
matched pairs sample test
test for the difference between population proportions
Problems and Certificates:
1. Certificates
Certificate for Hypothesis Testing (Means - p value) (Lesson 7.1)
Certificate for Hypothesis Testing (Means - Z value) (Lesson 7.2)
Certificate for Hypothesis Testing (Means – t value) (Lesson 7.3)
Certificate for Hypothesis Testing (Proportions - p value) (Lesson 7.4)
Certificate for Hypothesis Testing (Proportions - Z value) (Lesson 7.5)
2. Textbook Problems – 7.6; 7.9 (also do problem 7.9a under the assumption that you do not
believe that the population variances are equal); 7.32
3. Syllabus Problem – K
IX. Chi-Squared Tests and Analysis of Variance
Textbook Reading: Chapter 7 (section 7.4) and Chapter 8 (excluding section 8.1)
Topics:
Goodness of Fit - observed distribution compared to theoretical distribution
Goodness of Fit - test for independence of variables
One Factor Analysis of Variance: sum of squares within groups, sum of squares between
groups, and sum of squares total
Two Factor Analysis of Variance: sum of squares for each factor, sum of squares error, and
sum of squares total
Problems and Certificates:
1. Certificates
Certificate for Chi-squared test for Association (i.e.: Independence) (Lesson 7.9)
Certificate for Chi-squared test Goodness of Fit (Lesson 7.10)
(Textbook Problems on next page)
2. Textbook Problems: 7.42; 7.43 a,b,c; 7.47a (First, answer problem 7.47a by using Excel’s
one-factor ANOVA. Print your output. On the same page as your output, under the Excel
results, sketch by hand the critical region and clearly state the decision. Second, suppose that the
six lines in 7.47 represent six different states from which the representatives came. Use Excel
and two-factor ANOVA (without replication) to test at the five percent level
(i) whether average performance differs with customer representative background, and
(ii) whether average performance differs with original state of residence.
Print your output. On the same page as your output, under the Excel results, sketch by hand the
critical region for each test and clearly state the decision for each test.)
Using Excel for ANOVA:
1. If the analysis toolpak is not already set up on Excel:
Click tools, click add-ins, click the check box for analysis toolpak, click ok.
2. To run Excel’s one-factor ANOVA once the analysis toolpak has been set up:
Enter your data on the spreadsheet. Then click tools, click data analysis, click “ANOVA: Single
Factor,” specify input range, type in test level (alpha), click output range and specify, click ok.
3. To use Excel to do two-factor ANOVA, follow the one-factor instructions above, except instead
of clicking “ANOVA: Single Factor,” click “ANOVA: Two-Factor without Replication.”
[Note: The computer tutorial also has a module on single-factor ANOVA, which you may want
to explore for additional practice in this area. The module does not, however, give you the
opportunity to clearly express the conclusions of the analysis of variance test. For this reason, a
written homework problem on single-factor ANOVA is used instead of the ANOVA certificate.]
SYLLABUS PROBLEMS:
A. Suppose a vice president is examining factory A’s production levels. The numbers are given
below for a sample of 30 days.
Quantity Produced
(0, 10]
(10, 20]
(20, 30]
(30, 40]
(40, 50]
Number of Days
7
9
8
4
2
i. Draw the histogram or bar graph for the data above. Show the absolute frequency on the
left vertical axis and the relative frequency on the right vertical axis.
ii. Determine the mean and median production levels, as well as the standard deviation and
the coefficient of variation.
iii. Suppose another factory, call it B, has a mean production level of 24 with a standard
deviation of 13. What is the coefficient of variation?
iv. Which factory, A or B, has the higher absolute dispersion of production? Which factory
has the higher relative dispersion of production?
B. A statistics professor wants to choose a textbook and a software package for her students.
The professor is considering 6 textbooks and 3 software packages. How many different
pairs of textbooks and software packages are possible?
C. A professor has 10 questions on a topic. The students will only have enough time to answer
6 of the questions. How many different sets of 6 questions can he choose for the test?
D. If 10 questions are randomly arranged on a test, how many arrangements are possible?
E. Suppose you have a deck of 20 cards numbered 1 to 20. You choose a card at random. What
is the probability that the number on the card
i. is a 9?
iii. is more than 12?
ii. is less than 6?
iv. is at least 8 and at most 10?
F. A student business club wants to invite 4 speakers during the current year. They have a long
list of speakers from which to choose. Of the potential speakers, 50% are economists, 30%
are in information science, and 20% are accountants. If they select 4 names at random, what
is the probability that they will have 2 economists, 1 information scientist, and 1 accountant?
G. Using the following data, compute
i. the mean & variance of X.
ii. the mean & variance of Y.
iii. the covariance & correlation coefficient of X & Y.
iv. the mean & variance of X-3Y.
X
Y
|
0
1
2
---------------|-----------------------------------------0
|
0.1
0.1
0.0
1
|
0.1
0.5
0.0
2
|
0.0
0.0
0.2
H. The starting salary of the100 business majors, who recently graduated from a particular
university, has a mean of $25,000 and a standard deviation of $5,000. What are the mean and
standard deviation of the average salaries for all possible samples
i. of size 25?
ii. of size 50?
iii. of size 100?
I. Consider the following data. Five stock market analysts with only a high school diploma
each made an investment. The sample mean return for these analysts was 6 percent. Five
stock market analysts with MBAs also made investments. The sample mean return for this
group was 8 percent. Calculate the 95% confidence interval for the difference in returns for
high school graduates and MBAs,
i. if the sample variances for the high school graduates and MBAs are 0.36 and 0.25
respectively, assuming the population variances are believed to be equal.
ii. if the sample variances for the high school graduates and MBAs are 0.36 and 0.25
respectively, assuming the population variances are not believed to be equal.
iii. if the population variances for the high school graduates and MBAs are 0.36 and 0.25
respectively.
J. Consider two cold medications. Suppose that 600 people are given medication A; 390 get
symptom relief within an hour of taking the medicine. Suppose also that 700 people are
given medication B; 420 get relief within an hour. Calculate the 95% confidence interval
for the difference in proportions of the populations that would get relief from the two
medications.
K. Suppose that in a sample of 600 airline passengers at a Mexican resort, 250 reported
purchasing silver jewelry. From a sample of 400 airline passengers at a different Mexican
resort, 200 reported purchasing silver jewelry. Test at the 1% level whether the proportion
of tourists purchasing silver jewelry at the second resort is greater than the proportion of
tourists purchasing silver jewelry at the first resort.