Professor Karen Leppeloffice: 221 Quick Center

WIDENER UNIVERSITY
SCHOOL OF BUSINESS ADMINISTRATION

Intermediate Statistical Analysis (QA 252)
Syllabus –Fall 2012

Professor Karen LeppelOffice: 221 Quick Center

E-mail: ffice Telephone: (610) 499-1170

Web Page:

Office hrs: MTWTh 1:00-2:15 p.m.

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PREREQUISITE: Elementary Statistical Analysis - QA 251

CLASSROOM RULES: The School of Business Administration of Widener University seeks to prepare students for successful careers. In your career, you will be judged both on your competence and on your professionalism, which includes showing respect for others and taking responsibility for your actions. This course is a training ground not only for analytical thinking, but also for professionalism. Consequently, you are expected to act according to the following rules.

Do:

Attend class regularly and punctually.
Remain in the classroom for the duration of the class.
Remain awake and attentive throughout the class.
Bring to class appropriate materials and tools, such as notes and writing utensils.
Come to class prepared, having completed readings and other assignments.

During class meetings, do NOT:

engage in extraneous and distracting conversation.
talk on cell phones or send text messages.
do work pertaining to other courses.
Send/read e-mail, surf the internet, play computer games, etc.

Students who behave inappropriately will be asked to promptly discontinue the behavior or leave the classroom. Habitual violators will be required to meet with the Assistant Dean of the School of Business Administration to discuss the situation. If no acceptable resolution is achieved, the matter will be forwarded to the campus judicial system.

COURSE OBJECTIVES: This course, combined with EC 251, is designed to provide students with the basic statistical tools for decision-making. These tools include hypothesis testing, analysis of variance, chi-square tests, simple and multiple regression, time-series analysis, and nonparametric statistics.

LEARNING OBJECTIVES: At the completion of this course, the student should be able to:

(1) Perform hypothesis testing on population means, comparisons of population means, population proportions, and comparisons of population proportions;

(2) 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.

(3) Perform one-factor and two-factor analysis of variance;

(4) Calculate a simple regression and the associated statistics, and analyze and interpret the output of simple and multiple regression;

(5) Understand the trend, seasonal, cyclical, and irregular components of time-series; use the ratio-to-moving-average method to calculate seasonal indices, and seasonally adjust a time-series.

(6) Perform the following nonparametric tests: the Wilcoxon rank sum test, the Wilcoxon signed rank test, the Kruskal-Wallis test, and the runs test. (if time allows)

TEXTBOOK AND SOFTWARE:

Basic Business Statistics: Concepts and Applications, 12th ed., by Berenson, Levine, and Krehbiel, binder-ready with MyStatLab, Published by Prentice Hall. ISBN 0132780704.

LECTURE NOTES:
Notes are provided at my website: . In order to perform activities, students are required to bring the notes to class in either printed form (six-slides to a page is recommended) or in digital form on an electronic device.

COURSE POLICY:

Exams: There will be three exams and a final exam. The three exams will each count 16% of the final course grade while the final exam will count 26%. The final exam covers the material from the entire course. The three exams will be given after syllabus sections II, IV, and VI. Depending on the performance of the class, exam grades may be curved. Adjusted grades will be determined based on the relative position in the appropriate grade range. (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.

MyStatLabHomework: Students are required to do exercises on MyStatLab. To get full credit for an exercise, it must be done by the date specified. The MyStatLab homework counts for a total of 16% of the course grade.

Textbook Reading: In addition to the MyStatLab homework, the syllabus specifies parts of the textbook that you are required to read for each section of the course. It is important to do the reading. Why? We learn better if we see/hear material multiple times in multiple ways. Reading the textbook helps to reinforce and clarify what is presented in the lecture.

Group projects: Throughout the semester, students will be working on problems in small groups. In addition, each group will be required to do a project that will be graded. A written analysis of the results of the project is required. In addition, a presentation of the results must be made to the class. This project counts for 10% of the course grade. The grade of an individual student on the project will be adjusted for the contribution of that student to the group.

[CAUTION: Do not wait until the last minute to do the assignments. They take time!]

Summary of course grade determination:

3 exams each worth 16%48%

final exam 26%

MyStatLab homework 16%

group project 10%

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100%

PREPARATION FOR THE COMPREHENSIVE BUSINESS EXAM:

All students majoring in the School of Business Administration (SBA) are required to take a comprehensive business exam in their senior year. This exam covers the material from the required business courses that all SBA students must complete regardless of their major. It includes this course. Student learning outcomes of this course which are included on the comprehensive business exam are as follows:

Hypothesis testing on means and proportions
Chi-squared tests for goodness of fit and independence
Analysis of Variance
Regression analysis
Time series: seasonal, cyclical, trend, and random/irregular components

In order to effectively and efficiently prepare for this exam and increase your chances of performing well, you will want to take the steps listed below. Doing so will help to minimize your workload in your senior year. These strategies are also effective at improving performance in individual courses including this one.

1. Engage in study habits that promote long-term retention of the material in your courses and that minimize the amount of studying that will be needed later. Experts in learning and memory have found that reviewing notes soon after the material is presented significantly improves retention. Cramming shortly before an exam is NOT an effective means of promoting long-term memory.

2. Keep the books and notes from your required business courses. They will help you to review the material and serve as good references.

SKILLS OUTCOMES:

(1) Quantitative Skills:

(a) Skills-In: Background in Algebra and Elementary Statistical Analysis.

(b) Skills-Out: Ability to perform statistical tests, do regression analysis, and seasonally adjust time-series data.

(2) Computer Skills:

(a) Skills-In: Basic knowledge of the computer keyboard.

(b) Skills-Out: Ability to use a spreadsheet computer package to perform statistical analysis and interpret the output.

(3) Skills at Working in Groups:

(a) Skills-In: Basic communication skills.

(b) Skills-Out: Ability to work with others to analyze and solve a statistical problem.

TUTORING AND OTHER ACADEMIC ASSISTANCE: Students who need tutoring or could use assistance with study skills or time management are encouraged to contact Academic Support Services at522E. 14th Street (Pineapple House) (610-499-1267).

LEARNING TECHNIQUES:

lectures, group problem-solving, individual problem-solving

COURSE OUTLINE:

I. Hypothesis Testing on Means and Proportions – One Sample

Textbook Reading:
Chapter 9

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

Practice Problems:
Type I and Type II Errors
Valid Null and Alternative Hypotheses
One-Sample Hypothesis Testing

Problems on MyStatLab:

alpha and beta

p-value calculation 1

p-value calculation 2

p-value calculation 3

test mean w popvar

test mean wo popvar 1

test mean wo popvar 2

test prop

II. Hypothesis Testing on Means and Proportions – TwoSample

Textbook Reading:
Chapter 10

Topics:

tests for the difference between population means for independent samples: population variances known, population variances unknown, population variances unknown butbelieved equal

matched pairs sample test

test for the difference between population proportions for independent samples

test for difference in population variances for independent samples

Practice Problems:
Two-Sample Hypothesis Testing

Problems on MyStatLab:

test means diff w popvar

test means diff – pool

test means diff nopool

test: paired t

test prop diff

test diff var

III. Chi-Squared Tests

Textbook Reading:
Chapter 12 (sections 12.1-12.3 and 12.5 only)

Topics:

Goodness of Fit - observed distribution compared to theoretical distribution: uniform, Poisson, other historical, normal

Goodness of Fit - test for independence of variables

Hypothesis testing for the variance

Practice Problems:
Chi-squared Tests

Problems on MyStatLab:

goodness-of-fit test

chi-squared test ofindep

variance hypoth test

IV. Analysis of Variance

Textbook Reading:
Chapter 11 (excluding section 11.2)

Topics:

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, sum of squares interaction

Practice Problems:
Analysis of Variance Hypotheses
ANOVA Tables
Analysis of Variance Testing

Problems on MyStatLab:

anova: one factor

anova: two factor

V. Simple Regression Analysis

Textbook Reading:
Chapter 13

Topics:

estimating simple regression line

Gauss-Markov theorem: best, linear, unbiased estimates

(Topics continue on next page.)

sum of squares regression, sum of squares error, and sum of squares total

standard error of the regression or standard error of the estimate

coefficient of determination - adjusted for degrees of freedom and unadjusted

test for whether the slope coefficient is zero

test for whether the correlation coefficient is zero

forecasting intervals - individual case, mean of many cases

Practice Problems:
Simple Regression

Problems on MyStatLab (see tips below):

regress: simple – part 1

regress: simple – part 2

regress: simple – part 3

regress: simple – part 4

Tips for the mult-part simple regression problem on MyStatLab:

The data and the questions for this problem are repeated below so you can set up an Excel spreadsheet and work on the problem before entering your answers on MyStatLab.

Problem: A store manager wants to know the relationship between weekly sales (in hundreds of dollars) and shelf space (in feet) devoted to a particular type of product. He gathers the data as shown below.

shelf space / weekly sales
5 / 2
10 / 2
15 / 3
20 / 3
25 / 5

Part 1. (simple regression line: calculation and interpretation)

a. Use a spreadsheet to estimate the slope and intercept for the regression of sales on shelf space (to three decimal places). The slope is ______. The intercept is ______.

b. To three decimal places, eight feet of shelf space would be expected to generate ______hundred dollars of weekly sales.

c. An additional foot of shelf space would be expected to generate an additional ______hundred dollars of weekly sales.

Part 2. (slope coefficient: significance and confidence interval)

a. To perform a t-test on the significance of the regression on shelf space, the appropriate critical value (to four decimal places) is ______.

b. To perform a t-test on the significance of the regression on shelf space, the value of the test statistics (to three decimal places) is ______.

c. When you perform the test on the significance of the regression coefficient on shelf space, should you reject the null hypothesis? _____

d. Your conclusion from the test on the significance of the regression coefficient on shelf space is the slope of the regression line _____ (is/is not) zero.

(Problem continues on next page.)

e. The left side (lower limit) of the 95% confidence interval for the slope of the regression line (to three decimal places) is ______.

f. The right side (upper limit) of the 95% confidence interval for the slope of the regression line (to three decimal places) is ______.

Part 3. (coefficient of determination and correlation coefficient)

a. To three decimal places, the unadjusted coefficient of determination is ______.

b. The coefficient of determination indicates which of the following?

___the proportion of the variation in shelf space that is explained by the regression on weekly sales.

___the proportion of the variation in weekly sales that is explained by the regression onshelf space.

c. Calculate the correlation coefficient r to three decimal places. ______

d. Are the sign of the slope in the estimated regression line and the sign of the correlation coefficient the same or opposites? ______

e. The sign of the slope of the correlation coefficient in this problem indicates that when the amount of shelf space devoted to a product increases, the weekly sales from the product would be expected to ______(increase, decrease).

f. To perform a t-test on the significance of the correlation coefficient, the appropriate critical value (to four decimal places) is ______.

g. To perform a t-test on the significance of the correlation coefficient, the value of the test statistic (to three decimal places) is ______.

h. When you perform the test on the significance of the correlation coefficient, should you reject the null hypothesis?

i. Your conclusion from the test on the significance of the correlation coefficient is that the correlation coefficient between shelf space and weekly sales ______(is, is not) zero.

Part 4. (forecasting intervals)

For 95% forecasting intervals for this problem, the t-value (to four decimal places) is ______.
To three decimal places, the point estimate for the weekly sales expected from a product if 8 feet of shelf space is devoted to the product is ______.
To four decimal places, the standard error of the forecasting interval for weekly sales of an individual store devoting 8 feet of shelf space to a particular product is ______.
To three decimal places, the left side (lower limit) of the 95% forecasting interval for weekly sales of an individual store devoting 8 feet of shelf space to a particular product is ______.
To three decimal places, the right side (upper limit) of the 95% forecasting interval for weekly sales of an individual store devoting 8 feet of shelf space to a particular product is ______.
To four decimal places, the standard error of the forecasting interval for the mean weekly sales of many stores devoting 8 feet of shelf space to a particular product is ______.
To three decimal places, the left side (lower limit) of the 95% forecasting interval for the mean weekly sales of many stores devoting 8 feet of shelf space to a particular product is ______.

(Problem continues on next page.)

To three decimal places, the right side (upper limit) of the 95% forecasting interval for the mean weekly sales of many stores devoting 8 feet of shelf space to a particular product is ______.

VI. Multiple Regression Analysis

Textbook Reading:
Chapter 14 (excluding sections 14.5 and 14.7)

Topics:

standard error of the regression or standard error of the estimate

coefficient of determination - adjusted for degrees of freedom and unadjusted

test for whether a particular slope coefficient is zero

test for whether all slope coefficients are zero

dummy variables

multicollinearity

autocorrelation and Durbin-Watson statistic

Practice Problems:
Multiple Regression

Problems on MyStatLab:

regress – mult – part 1

regress – mult – part 2

regress – mult – part 3

dummy variable interpret

Durbin Watson test

VII. Time Series

Textbook Reading:
Chapter 16 (page 666 through the middle of page 675 only)

Topics:

four components: trend, seasonal, cyclical, and irregular

estimating a linear trend using ordinary least squares

calculating seasonal indices and seasonally adjusting a series using ratio to moving average method

exponential smoothing

Practice Problems:
Time Series

Problems on MyStatLab:

seasonal indices (see tips below)

exponential smoothing

Tips for the seasonal indices problem on MyStatLab:

The data in this problem are repeated below so you can print the information and work on it.

quarter 1 / quarter 2 / quarter 3 / quarter 4
year 1 / 270 / 253 / 243 / 134
year 2 / 285 / 258 / 256 / 126
year 3 / 286 / 256 / 259 / 123
year 4 / 291 / 265 / 256 / 142
year 5 / 289 / 271 / 263 / 165

I. To do the problem, set up a table like the one on the PowerPoint lecture slides. After completing the table, go to MyStatLab and answer the questions.

To help you verify that you are doing your calculations correctly, the first numbers for each column of your table are provided here.

First number in 4-qtr MA column (year 1, quarter 3 row): 225.0000.

First number in centered 4-qtr MA column (year 1, quarter 3 row): 226.8750.

First number in 100*Y/MA column (year 1, quarter 3 row): 107.1074.

First number in adj. seas. indices column (year 1, quarter 1 row): 123.3652.

First number in adj. series column (year 1, quarter 1 row): 218.8624.

II. You may want to use an Excel spreadsheet to do the calculations for the time series seasonal indices problem. However, the moving averages can be a bit confusing because you can’t put the numbers between the spaces, only in the spaces. Whether you do it by calculator or Excel spreadsheet, be sure to clearly label your columns and other work to minimize confusion. Excel’s Moving Average module can be used to do part of the calculations for the problem. (Getting the moving averages in the appropriate rows using Excel can take a little thought.) In the Data tab, click on Data Analysis, Moving Average, OK. InputRange is the column of data for which you’re computing the moving average. Suppose your headings or labels are in row 1. Then if you indicate, say, c2:c21 (not c1:c21), don’t check the box marked labels in first row. The interval would be 4 for four quarters. Output range is the beginning of the section of the column where the results will go, for example, d2. You will need to delete some “NA”s. You will need to cut and paste to get the results where they belong. For 4 quarters, the first moving average should be between the second and third value of the original series and on a computer spreadsheet, you line it up next to the third value. Now you have uncentered moving averages (MAs). To center the MAs, do essentially the same thing, using the MA positions for your input range and 2 for the interval, since you’re averaging 2 MAs this time instead of 4 series values. After Excel computes the results, cut and paste so that the first centered MA is on the same line as the third value of the original series. Now you have the centered MAs. You still have quite a bit of work to do to complete the adjusted seasonal indices and seasonally adjust the series. This is as far as the Excel Moving Average module takes you. You can complete the problem on a spreadsheet, but you need to put together the steps yourself. Again, follow the steps shown in the lecture. (Unlike the lecture, however, when you are calculating the seasonal indices, for each quarter, be sure to drop the highest and lowest values and average the remaining two values.)