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