Last Day - 7 December 2006

Review

Mini Exam - 5 December 2006

Here are the recordings for the mini exam we had in class.

Section 001
Section 002

Also, for Section 001, here are the last few pages for Chapter 13.

Section 001

Chapter 13: 28 November 2006

We continued our discussion on Linear Regression  and Correlation. We saw that the linear regression models are generally valid only for the range of data observed.

Section 001
Section 002

Chapter 13: 16 November 2006

We started our discussion on Linear Regression and Correlation. We saw examples of scatter plots, and correlation coefficients.

Section 001
Section 002

Additional Review Session

Some students have expressed an interest in having an additional review session. I can do that on the following days and time:

This Friday (11/17): 2 - 3
Weekend: Usually in the afternoon
Monday: 1-3

Please leave your comments if you are interested, and what times are suitable.

The review session will be on Friday from 3 to 4. Please meet at A401 BSA (my office).

Review: 14 November 2006

We continued our review for Exam 3, and concentrated on Confidence Intervals.

Section 001
Section 002

Review: 9 November 2006

We reviewed hypothesis testing today. This is part of the review for Exam 3.

Section 001
Section 002

Chapter 8: 7 November 2006

We completed our discussion on hypothesis testing today.

Section 001
Section 002

Chat Tool

I have now added a new tool to the blog. You can chat right here :-) Try it out.

Chapter 8: 2 November 2006

Today, we started our discussion on Hypothesis Testing. We saw the three types of hypothesis, and definition of rejection region, critical values, and p-values.

Section 001
Section 002

Chapter 7: 31 October 2006

We finished our discussion of confidence intervals by talking about one-sided intervals. We saw examples using both the T and the standard-normal tables.

Section 001
Section 002

Chapter 7: 26 October 2006

We continued our discussion on confidence intervals, and introduced the t distribution. The t distribution is used when we don't have the population standard deviation, and instead use the sample standard deviation s. All other assumptions remain in calculating the confidence intervals.

As expected, Lecture123 in Section 2 crashed. But, I have been able to recover most of it, so it is in two parts. The easiest way is to just listen to Section 001 lecture.

Section 001
Section 002 - part 1
Section 002 - part 2

Chapter 7: 24 October 2006

Today's topic was on interval estimation. Specifically, we talked about confidence intervals. We made assumptions on the distributional form, and that we knew σ. In the next class, we will relax some of these assumptions.

As with technology, things did go wrong. I completely lost Section 001 lecture. Thankfully, the Section 002 lecture worked. So, please use that to listen to your lectures.

Section 002

Review - Exam 2: 19 October 2006

Exam 2:

• 25 questions
• 6-8 questions from Chapter 1-3, rest from 4-6.
• 4-5 interpretation type questions. Know your definitions.

Section 001
Section 002

Chapter 6: 17 October 2006

We finished our discussion of sampling discussions by discussing properties of estimators.

• An estimator is unbiased if on average the value of the estimator is equal to the parameter it is estimating.
• An estimator is consistent if the larger the sample size, the closer is the value of the estimator to the parameter it is estimating.
• An estimator is efficient, if it has the smallest variance among other unbiased estimators.

Section 001
Section 002

Additional Problems for Exam 2 - Section 001

Chapter 6: 12 October 2006

We continued our discussion on sampling distributions. We saw four important points:

1. The average of all the sample means is equal to the population mean μ. That is, E(Xbar) = μ
2. The variance of the sample mean is equal to the variance of the population divided by the sample size. That is, σ²_xbar= σ²/n.
3. When the population is normally distributed, the sample mean distribution is also normal. That is, if X ~ N, Xbar ~ N.
4. When we don't know the distribution of the population, the distribution of the sample mean is approximately normally distributed for large sample sizes. This is called the central limit theorem.

Section 001
Section 002

Chapter 6: 10 October 2006

Today's lecture, or at least I tried to, was on Sampling Distributions. The idea behind sampling distributions is to understand the behavior of the sample mean. By doing that, we can then be able to predict the population mean more accurately. As an exercise, I asked each group to calculate the population mean (N=8). I then asked each group to take samples of size n=7, and for each sample, calculate the sample mean. You should have observed the following results:

The average of the sample means, i.e., E(Xbar) = μ, the population mean. In the next class, we will talk about other properties of the sampling distribution of the sample mean. Today's Section 001 lecture may be a little off the chart. Those who attended know why, I hope :-)

Section 001
Section 002

Chapter 4: 5 October 2006

We continued our discussion on the Normal Distribution. I have posted several additional problems for Exam 2, and also please look at the sample problems of my Wednesday, September 13, 2006 blog post. That contains more questions on the Normal Distribution. Here are the lectures:

Section 001
Section 002

Exam 1 Results

Count:	337
Average:	39.5
Median:	40.0
Maximum:	50.0
Minimum:	19.3
Standard Deviation:	5.87

Glossary

I have now added a link to a glossary of terms used in our class. This list is not complete, but I will continue to add terms as the semester progresses.

Chapter 4: 3 October 2006

Today, we continued our discussion on random variables, and specifically, continuous random variables. We started our discussion on Normal Distribution. Specifically, we saw the properties of the Normal distribution, and how to convert to Standard Normal, and then use the tables to determine probabilities. The lectures are here:

Section 001
Section 002

I also asked you to look over Exam 1. Please give me specific examples of the types of questions you are having trouble with it, and how I can help.

Chapter 4: 28 September 2006

Today, we discussed random variables, and probability distributions. We saw examples of discrete distributions, and started discussing the Normal distribution.

Section 001
Section 002

Exam 1 review: 26 September 2006

We reviewed chapters 1-3. There were some techical problems in Section 001, but I still managed to capture the session, just not in Lecture123. Section 001 students can listen to Section 002, if you want to do it through Lecture123, or directly in the links given below:

Section 001
Section 002

Answers to additional problems for exam 1

Q. You are given the following data: 23,34,11,40,25,47
assuming that these data reflect the population of interest, these
data can be considered symmetric.
A. Calculate the mean and median. If the values are the same, then the data are symmetric.
Q. If a set of data has 1,500 values, the 30th percentile
value will correspond to the 450th value in the data when the data
have been arranged in numerical order.
A. True. .30 x 1500 = 450. That indicates that the 450 values is the 30th percentile.
Q. A nuclear power plant produces a large amount of heat that is discharged into the water system. This heat can raise the temperature of the water system which leads to an increase in the concentration of chlorophyll-a and thus a longer growing season. To study this effect, water samples were collected monthly for one year at 3 stations and the concentration of chlorophyll-a (in milligrams per liter, mg/liter) was measured. Station 1 is closest to the source of discharge while Station 3 is furthest away. The data were used to produce the following side-by-side boxplots. What is (approximately) the largest concentration of chlorophyll-a in mg/liter for Station 2?

A. The largest concentration for Station 2 appears in March. That value is approximately 17.
Q. Suppose a study of houses that have sold recently in your community
showed the following frequency distribution for the number of bedrooms:

Bedrooms Frequency
1 1
2 18
3 140
4 57
5 11
Based on this information the mean number of bedrooms in houses that
sold is approximately 3.26. Explain?
A. The first column is the number of bedrooms, and the second column is the count or frequency, i.e., how many houses with such bedrooms. Therefore, the total number of bedrooms there are:

1x1 + 2 x18 + 3x140 + 4x57 + 5x11 = 740

You need to divide this total by the total number of houses to get the average number of bedrooms per house:

Average = 740 / (1 + 18 + 140 + 57 + 11) = 740 / 227 = 3.26

Chapter 3: 21 September 2006

Today, we completed chapter 3 by talking about Standard Deviation, and Coefficient of Variation. We also discussed linear transformations, and a special case, standardization.

Lectures:

Section 001
Section 002

Additional Problems for Exam 1

Section 001
Section 002

Extra Problems for Exam 1

I have posted additional practice problems for Exam 1. Check your Vista site under Assessments/Practice Problems.

Chapter 3: 19 September 2006

Today, we continued our discussion on measures of location, percentiles, and started measures of variation. Specifically, we saw Range, Interquartile Range (IQR), Variance and Standard Deviation. We discussed limiations of the range, and IQR, and started discussing Variance.

Based on suggestions from you, I will try and include more examples like the Quiz in my lectures. Please come prepared on Thursday with any doubts, questions for Exam 1. I felt that the Section 002 lectures went much better than Section 001 for various reasons including audio issues. I would suggest that if you are reviewing the lectures, try Section 002 first, even if you are in Section 001.

Section 001
Section 002

Chapter 3: 14 September 2006

Today, we saw different measures of summarizing data. We discussed measures of location like mean, median, and mode. We saw the need to define and look at data in different ways. The lectures can be found here:

Section 001
Section 002

I also answered some questions on Practice Quiz 1. The lectures are here:

Section 001
Section 002

Additional Sample Problems

There are some additional sample problems available. You will need adobe acrobat to view and print them.

Sample Problems
Answers to Sample Problems

Note that the Chapter headings don't really match your notes. For Quiz 1, from the Sample problems, do:

• Page 1 - all problems
• Page 2 - 1 through 5

Practice Quiz 1 and Quiz 1

I decided to post the questions and answers here, so it is available to all students:

Q. A researcher would like to estimate the proportion of adult voters who are in favor of Proposition A. The population of adult voters is stratified into males and females. Sixty percent of the population is known to be male. A stratified random sample of size 100 (50 males and 50 females) is taken from the population. If the sample proportion of males favoring Proposition A is 0.17, while the sample proportion of females favoring Proposition A is 0.62, then estimate the proportion of adult voters in the population favoring Proposition A. Give you answer accurate to two decimal places. For example, if your answer is 40%, state your answer as 0.40.
A. Two things to remember. First, the answer they want is the proportion in the population. Secondly, we know the proportion in the sample. We know that 0.17 of males (from the sample) prefer Proposition A. The percentage of males in the population is 0.60. Thus, of the males, 0.60 x 0.17 prefer Proposition A. Similiarly, 0.62 of females prefer Proposition A, and .40 of the population contains Females. Thus, of the females, 0.40 x 0.62 prefer Proposition A. Adding them, 0.60 x 0.17 + 0.40 x 0.62 = .35. You might have different numbers, but the logic should be the same.

Chapter 1: 12 September 2006

Today, we discussed sampling, and the importance of collecting good data. We discussed four different probability sampling methods: Simple random sampling, stratified sampling, cluster sampling, and systematic sampling. We also discussed Qualitative and Quantitative data. Your online lectures are now available:

Section 001
Section 002

Also, class notes for Chapter 3 are now available here.

Chapter 1: 7 September 2006

In today's lecture, we discussed p-values. We saw that once p-values were calculated, we could decide on which hypothesis to conclude by comparing it to the type I error. This lecture concludes the overview on the decision making process. That is, we discussed how to set up the hypothesis, collect data, analyze the results, and come to a conclusion. We will continue our discussion with sampling.

The multimedia lectures can be found at:

Section 001
Section 002

Chapter 1: 5 September 2006

Today, we discussed errors in decision making. We saw the difference between Type I (α) and Type II (β) errors. An example was used to illustrate how the decision rule affects these errors. We concluded by examining the concept of p-values. We will continue this discussion in the next class. The links for the lectures are given below.

Section 001
Section 002

Chapter 1: 31 August 2006

Today was an introduction to Statistical Concepts, and how we test theories. Specifically, we introduced the concept of Null and Alternative hypothesis, and discussed under what circumstances we choose one over the other. The links for the multimedia lectures are given below:
Section 001
Section 002

First Day

The multimedia lectures are now available from the first day of class. As the two sections will be in sync, I will generally only post the link from one of the two lectures for each class. For this particular day, I am posting both the 12:30 - 1:45 (Section 001), and 3:45 - 5:00 (Section 002) lectures.

Section 001
Section 002
Click for Audio and Video podcasts:

I will send you an e-mail with your community ID, and access key so that you can access these lectures.

Also, some while some students could not hear me well today, it will not be possible for me to use a microphone, as this will interfere with the recordings in class.

Chapter 1 Notes

Lecture notes for Chapter 1 are now available in powerpoint and pdf formats. After your class, I will post the link for the multimedia lectures. Note that the multimedia lectures will contain all information on the lecture notes, as well as any information I write and speak in class. You will be able to print these multimedia lectures, in addition to listening to them.

First Post

This is my first attempt at using blogs to support teaching. This blog will primarily contain links to the multimedia lectures for my Fundamentals of Business Statistics course. The lectures in class will be captured using Lecture123, and can be viewed over the web or as a podcast. After each class, I will post the link to that lecture. If you are using software like iTunes, you can also subscribe to the feed by clicking on the RSS feed button at the bottom right of the blog.

Feel free to comment here. Though, if you have questions about the subject matter, do so as part of listening to the lectures using Lecture123. That way, both your question, and my response will be available to all students.