Lecture Notes on Sakai: Sequential Sessions   (Use your ID, and Password: Technical Difficulties: tross@ubalt.edu (40)837-5078)

FALL SCHEDULE

Notice that any late homework has zero value.

 Homework Assignment Sessions Dates Topics Homework Due Date 1 Week of Mondays January 21 and January 28 What Is Business Statistics? Monday February 4 2 Week of Monday February 4 Descriptive Statistics Monday February 11 3 Week of Monday February 11 Probability and Expected Values Monday February 18 4 Week of Monday February 18 Discrete & Continuous Distributions Monday February 25 5 Week of Monday February 25 Sampling Distribution and the CLT Monday March 4 6 Weeks of Mondays March 4, and March 11 Week of Monday March 18 is the Spring-Break Statistical Inference Monday March 25 7 Weeks of Mondays March 25 and April 1 Review, Practice, First Exam. Monday April 8 8 Week of Monday April 8 Analysis of Variance Monday April 15 9 Weeks of Monday April 15, and 22 Regression Analysis Monday April 29 10 Weeks of Mondays April 29 and May 6 Review, Practice, Final Exam. Monday May 13

1. Here is my Textbook Solution (60%)
2. Here is my Computer Implementation (20%)
3. Here is my Answer to the Lecture Note Question (10%)
4. Statement: I have already posted my A Few-minutes Paper (10%)

Collaborative Learning: It is a fact that we learn from each other, and it is good to rub and polish our mind against that of others.
The following are a sample of HW submitted by your classmates:

#### Homework Assignments to Do Before Each Class Meeting and Sample Tests

We will follow the following sequential sessions (Not a weekly-schedule) of topics.

1. An Overview of Business Statistics (Due date: February 4)

Introduction: In this diverse world of ours, no two things are exactly the same. A statistician is interested in both the differences and the similarities, i.e. both patterns and departures.

Exploratory analysis of data makes use of numerical and graphical techniques to study patterns and departures from patterns. The widely used descriptive statistical techniques are: Stem & Leaf, Box Plot, Frequency Distribution, Empirical Cumulative Distribution, Histograms; and Scatter-diagram.

The actuarial tables published by insurance companies reflect their statistical analysis of the average life expectancy of men and women at any age. From these numbers, the insurance companies then calculate the appropriate premiums for a particular individual to purchase a given amount of insurance.

In examining distributions of data, you should be able to detect important characteristics, such as shape, location, variability, and unusual values. From careful observations of patterns in data, you can generate conjectures about relationships among variables. The notion of how one variable may be associated with another permeates almost all of statistics, from simple comparisons of proportions through linear regression. The difference between association and causation must accompany this conceptual development.

Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. The plan must identify important variables related to the conjecture and specify how they are to be measured. From the data collection plan, a model can be formulated from which inferences can be drawn.

Objectives: What is statistics and what can it do? The main objective of this unit is to orient you to the subject of Business Statistics. When you have successfully completed this unit, you will know what to expect from this course and you will have an overview of the topics involved in the weeks to come. In the course you will learn to use statistical techniques to investigate business situations, and you will gain a good understanding of statistical ideas and thinking.

Homework (Due date: February 4)

Read Ch (1-2), there's nothing much in Ch (1-2) to challenge you. It is an attempt to orient you to the subject of Business Statistics.
Read the Lecture Notes: Session 1.

Visit the following external Web sites:

After you did your reading assignment, and visiting the external Web sites, then write a 2-page essay entitled: "What is Business Statistics?" You essay should, among others, address the following questions:

• What is statistics?
• What benefits would you expect from using statistics?
• Is statistic a form of applied decision science under uncertainty?
• Does statistics make decisions?
• Why has statistics become more widely used in the past few decades?

2. Descriptive Statistics (Due date: February 11)

Introduction: Decision makers make better decisions when they use all available information in an effective and meaningful way. The primary role of statistics is to provide decision makers with methods for obtaining and analyzing information to help make these decisions. Statistics is used to answer long-range planning questions, such as when and where to locate facilities to handle future sales.

One must understand conceptually the meanings of measures of locations of the central tendency, e. g. mean, median, and mode, and measures of variability, e. g., range, variance, standard deviation, and coefficient of variation.

The problem most decision makers must solve is how to deal with the uncertainty that is inherent in almost all aspects of their jobs. Raw data provide little, if any, information to the decision makers. Thus, they need a means of converting the raw data into useful information. In this lecture, we will concentrate on some of the frequently used methods of presenting and organizing data.

Objectives: When you successfully complete this unit, you will be able to cite examples to show the importance of data and statistical summary measures in business. You will be able to use alternative methods and measures to describe sets of data so that the phenomena they represent can be more easily understood. You will be able to enter data, use the Web-based statistical computation functions to obtain descriptive statistics, and interpret results. You will be able to identify the formula used by the Web-based computer to make calculations and perform simple calculations with those formulas on a hand held calculator using the raw (or original) individual values. You will also be expected to recognize when data transformations are needed before attempting to represent magnitudes with the standard measures of location and dispersion. You need graph paper (Word.Doc) , graph paper (PDF) to present you density function and distribution function.

Visit the following external Web sites:

Homework (Due date: February 11)
Redo and then submit a written a step-by-step generalized solution summary for the following numerical examples: 2.5, 2.7, 3.1, 3.2, 3.8, and 3.14.

E-Labs and Computational Tools: Select a couple of JavaScript from the following list to perform some numerical experiment for deeper understanding of the concepts. For example, you may like checking your hand-computations for the homework problem(s), or checking the numerical examples from your textbook. Submit along with the rest of your Homework a short report entitle Computer Assignments describing your findings, no need to include any printout.

OR
Use Excel to perform your few computer implementation, for example Test for Unimodality for Problem 3.60. As an alternative you may use Stem-and-Leaf Plotter.

3. Introduction to Probability (Due date: February 18)

Introduction: Probability theory provides a way to find and express our uncertainty in making decisions about a population from sample information. Please, see the Chart given in the first week lecture note for the relevancy of Probability to Statistics.

Any generalization and extension of the results obtained from a random sample to the population contains uncertainties. How do you measure uncertainty? The answer is: By Probability measure.

Objectives: When you successfully complete this unit, you will be acquainted with the notion of a random variable and the basic rules of probability. You will be familiar with the expected values (means and variances) of a random variable and the sum of random variables. You will be able to articulate the difference between a mean calculated with relative frequencies and probabilities. You will be able to calculate means and standard deviations. You will be able to make applications to business and economics as well as personal financial situations (and in your Finance courses).

Read Ch. 4, and Ch. 5 sections 5.1, 2, 3, 4. Read the Lecture Notes: Session 3.

Visit the following external Web sites:

Homework (Due date: February 18)
Redo and then submit a written a step-by-step generalized solution summary for the following numerical examples: 4.8, 4.13, 4.15, 4.16, 5.2 â 5.4, 5.8, and 5.9.

E-Labs and Computational Tools: Select a couple of JavaScript from the following list to perform some numerical experiment for deeper understanding of the concepts. For example, you may like checking your hand-computations for the homework problem(s), or checking the numerical examples from your textbook. Submit along with the rest of your Homework a short report entitle Computer Assignments describing your findings, no need to include any printout.

OR
Use Excel to perform your few computer implementation.

4. Common Discrete & Continuous Distributions (Due date: February 25)

Introduction: A Random Variable is a quantity resulting from a random experiment that, by chance, can assume different values, such as, number of defective light bulbs produced during a week. Also, we said a Discrete random Variable is a variable which can assume only integer values, such as, 7, 9, and so on. In other words, a discrete random variable cannot take fractions as value. Things such as people, cars, or defectives are things we can count and are discrete items. In this unit, we will discuss Binomial distribution which a widely used distribution for discrete random variables.

A Continuous random is a variable can take on any value over a given interval. Continuous variables are measured, not counted. Items such as height, weight and time are continuous and can take on fractional values. For example, a basketball player may be 6.954 feet tall.

There are many continuous probability distributions, such as, uniform distribution, normal distribution, the t-distribution, the chi-square distribution, and F-distribution. In this unit, we will concentrate on the uniform and normal distributions.

Objectives: When you successfully complete this unit, you will be able to articulate the difference between probabilities associated with discrete and continuous random variables. You will be able to identify the use of discrete distributions in real and hypothetical situations. You will be able to identify the correct use of specific continuous distributions in real and hypothetical situations. You will know the general properties of the normal and t-distributions, and be aware of the existence and possible use of other continuous distributions like the Chi-square and F. You will be able to use available Web-based tools to obtain probabilities from these distributions.

Visit the following external Web site:

Homework (Due date: February 25)
Read Sections 6.1 â 6.3 and 6.5 of Ch. 6. Read the Lecture Notes: Session 4..
Redo and then submit a written a step-by-step generalized solution summary for the following numerical examples: 6.1 â 6.9, and 6.15

E-Labs and Computational Tools: Select a couple of JavaScript from the following list to perform some numerical experiment for deeper understanding of the concepts. For example, you may like checking your hand-computations for the homework problem(s), or checking the numerical examples from your textbook. Submit along with the rest of your Homework a short report entitle Computer Assignments describing your findings, no need to include any printout.

OR
Use Excel to perform your few computer implementation.

5. Sampling, Sampling Distributions & Estimation with Confidence (Due date: March 4)

Introduction: You may recall that there are several good reasons for taking a sample instead of conducting a census, for example, to save time, money, etc. Also, in the same lecture we said that if a for example, a marketing researcher is using data gathered on a group to reach conclusions about that same group only, the statistics are called descriptive statistics. For example, if I produce statistics to summarize my class's examination effort and use those statistics to reach conclusions about my class only, the statistics are descriptive. On the other hand, if a researcher collects data from a sample and uses the statistics generated to reach conclusions about the population from which the sample was taken, the statistics are inferential statistics. The data collected are being used to infer something about a large group.

In attempting to analysis the sample statistic, it is essential to know the distribution of the statistic. In this lecture, we are going to talk about the sample mean as the statistic. In order to compute and assign the probability of occurrence of a particular value of a sample mean, we must know the distribution of the sample means. In other words, how are sample means distributed? One way to examine the distribution possibilities is to take a population with a particular distribution; randomly select samples of given size, compute the sample means, and attempt to determine how the means are distributed.

Objectives: When you successfully complete this unit, you will be able to describe different methods of sampling and demonstrate how the Central Limit Theorem and sampling distributions are used for estimation in statistical analysis. You will be able to articulate what a sampling distribution is, and to explain the relationship between an estimator and the parameter being estimated. You will be expected to make statistical inferences and constructing confidence interval within practical business applications involving the estimation of mean and the variance s2 using the t (or z), and c2 (read, ki-square, it's not squared of anything, its name is Chi-square read, ki-square). There is no such thing as ki in statistics. I'm glad that you're overcoming all the confusions exist in learning statistics) distributions, respectively.

Read Ch. 7. and Ch. 8. Read the Lecture Notes: Session 5.

Visit the following external Web site:

• Quincunx to illustrate why normal densities are so frequently occurring natural phenomena

Homework: (Due date: March 4)
Redo and then submit a written a step-by-step generalized solution summary for the following numerical examples: 7.8, 8.4 â 8.8, 8.12 â 8.15, 8.19, 8.21, and 8.30

E-Labs and Computational Tools: Select a couple of JavaScript from the following list to perform some numerical experiment for deeper understanding of the concepts. For example, you may like checking your hand-computations for the homework problem(s), or checking the numerical examples from your textbook. Submit along with the rest of your Homework a short report entitle Computer Assignments describing your findings, no need to include any printout.

OR
Use Excel to perform your few computer implementation.

6. Hypothesis Testing and Statistics with Confidence (Due date: March 11)

Introduction: In the previous unit, our discussion partly was on sampling from a population, we have known the population, and calculated the chance (exact or approximate) that, for example, the average of the sample would be in some range. That is, a probability calculation. We also learnt, how to construction of confidence intervals for population parameters (mean and variance), which is working backwards from a sample to population, or to infer something about the population, of course, subject to some uncertainty. This is one of the most important and fundamental problems statistics addresses: how to estimate and make inferences about a parameter of a population based on a random sample taken from the population, using a CORRECT statistic method.

Because the value the estimator takes depends on the sample, the estimator's value is random, and will not typically equal the value of the population parameter. We need to understand how the value of the estimator varies for different possible samples to be able to say how close or how far from the parameter value the estimator's value is likely to be. That's essentially what a C.I. is for.

Now we turn on to test of hypotheses (claims) about mean and variance of a population or concerning comparison of these parameters for two populations based on random samples.

We learn that there is a duality between the test of hypothesis and construction of confidence interval. That is, instead of performing a test for a claimed value for the population parameter, we may construct a confidence interval, and then see if the constructed confidence interval contained the claimed valued.

Objectives: When you successfully complete this unit, you will be able to use sample data to test claims and statements about population (and comparisons of two populations) parameters (mean and variance). You will be able to specify the null and alternative hypotheses, select and calculate a correct test statistics, and use p-values in decision making. You will also be able to do all

Visit the following Web site:

Homework (Due date: March 11)
Read Sections 10.1 â 10.4 of Ch. 10, and Ch. 11.
Redo and then submit a written a step-by-step generalized solution summary for the following numerical examples: 10.7, 10.8, 10.11, 10.12, 10.16, 11.10, 11.12, 11.15, and 11.17

E-Labs and Computational Tools: Select a couple of JavaScript from the following list to perform some numerical experiment for deeper understanding of the concepts. For example, you may like checking your hand-computations for the homework problem(s), or checking the numerical examples from your textbook. Submit along with the rest of your Homework a short report entitle Computer Assignments describing your findings, no need to include any printout.

OR
Use Excel to perform your few computer implementation.

Spring Break: Week of Monday March 18: No Class Meeting.

7. Review Session: What have we learned up to now? Do Sample Exam at Lecture Notes Session 7. (Due date: March 25)

Preparation for the Test: Due date: April 1.

Your preparation is a very important undertaking in terms of integrating what you have learned each week in order to see the whole picture and inter-connectivity of the topics.

To prepare yourself for the actual test, you are advised to review all the topics we have covered, to review past homework assignment, and then prepare your own few pages of a summary sheet (see the course information). The process of producing a summary sheet, helps you to crystallize your mind to be reflective and responsive to any question posed to you about the topics you've learned in this course, it also helps you to reinforce the wholeness of the topics in your mind.

A good source for practice questions is the Web site Practice Questions, sections: Descriptive Statistics, Probability, Distributions, Making Inferences, and the Hypothesis Testings.

Exercise Your Knowledge on this Sample of Past Midterm Tests:

Past Midterm Exam (Word.Doc)

Solution (to some parts) submitted by one of your classmates

If you think you have prepared a better one, kindly send it to me via an attached email. Thank you.

8. First Examination April 8, Read the Examination Facts. The main purpose of taking the examinations is to find out how reflective your mind is in answering a set of questions correctly.

9. ANOVA (Due date: April 15)

Introduction: Analysis of Variance or ANOVA is a technique for comparing several populations means. We have already learned how to use the t-test (or z-test, for large samples) for test of hypothesis with respect to equality of means in two populations. Therefore, ANOVA is an extension of t-test for testing the equality of means in more than two populations. The conditions under which this test can be applied are as follows: Populations must has normal distributions, and Variations in the populations must be equal

In ANOVA we partition the total variation into two components: variation within each population, and variation between the populations. Under the above conditions, if these two components are the same magnitude, then there is no reason to reject that these populations are, in fact the same. That is, there are all normally distributed, having same mean and same variance.

Objectives: When you successfully complete this unit, you will be able to use sample data to test claims and statements about the means of several populations. You will learn the necessary conditions under which such a test would be valid.

Visit the following external Web site:

Homework (Due date: April 15)
Read Sections 14.1 â 4.4 of Ch. 14, and the Lecture Notes: Session 8.
Redo and then submit a written a step-by-step generalized solution summary for the following numerical examples: 14.3, and 14.4.

E-Labs and Computational Tools: Select a couple of JavaScript from the following list to perform some numerical experiment for deeper understanding of the concepts. For example, you may like checking your hand-computations for the homework problem(s), or checking the numerical examples from your textbook. Submit along with the rest of your Homework a short report entitle Computer Assignments describing your findings, no need to include any printout.

OR
Use Excel to perform your few computer implementation.

10. Regression, Covariance & Correlation (Due date: April 29)
11. Introduction: The statistics such as Covariance, Correlation, and Regression indicate mathematical linear relationship between two or more variables within the same population.

Objectives: This unit covers the statistical modeling of situations in which a response variable depends on one or several explanatory variables. When you successfully complete this unit, you will be able to identify situations in which there may be a linear relationship between a dependent variable y and an independent variable x. With paired data on y and x, you will be expected to use the method of least squares with the Web-based tools and Excel to estimate the linear relationship between these two variables; y values will then be predicted, and hypotheses about the slope or intercept will then be tested within this framework. You will be expected to interpret coefficients and other statistics produced by these computational tools.

Visit the following external Web site: Ordinary Least Squares

Homework (Due date: April 29)
Read Ch. 12. Redo and then submit a written a step-by-step generalized solution summary for the following numerical examples: 12.3, 12.7, 12.10, 12.12, 12.14

E-Labs and Computational Tools: Select a couple of JavaScript from the following list to perform some numerical experiment for deeper understanding of the concepts. For example, you may like checking your hand-computations for the homework problem(s), or checking the numerical examples from your textbook. Submit along with the rest of your Homework a short report entitle Computer Assignments describing your findings, no need to include any printout.

OR
Use Excel to perform your few computer implementation.

12. Review and Preparation for Final Test (Due date: May 6)

If you think you have prepared a better one, kindly send it to me via an attached email. Thank you.

Review all your past assignments. For practice questions visit the Web site Practice Questions, ALL sections including ANOVA, and Regression Analysis.

Exercise Your Knowledge on this Sample of Past Final Tests:

Past Final Exam (Word.Doc)

13. Final Examination (May 13) Read the Examination Facts.
14. After This Course Is Over: Statistical Concepts You Need For Life (Word.Doc).

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