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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.