Extra Office Hours

Please note that the TAs for our course (Sandy Wu and Majid Taghavi) will hold extra office hours at 2:30-5:30 pm, Tuesday, Dec 14, 2010.

I will also be available in my office on December 16 from 2:30 to 3:30 pm.

Summary for Week 12 (November 30 - December 2)

This week we started new Chapter 11 which is concerned with the relationship between two variables (usually, one independent and the other dependent).

We talked about covariance (not too useful by itself) and correlation coefficient (more useful).

We then moved on to a discussion of simple linear regression where the objective is to see if an independent variable (i.e., the student population in the example) can be used to estimate the value of the dependent variable (i.e., the monthly sales in the example). We calculated the regression equation's coefficients and performed an hypothesis test to see if the model was "significant."

We will complete our discussion of this chapter in the final week by learning about the coefficient of determination (r squared).

Summary for Week 11 (November 23-25)

We ended Chapter 9 with a discussion of hypothesis testing for equality of two variances. If the null hypothesis cannot be rejected, then the assumptions we made about the equality of variances in Chapter 9 are justified. The test statistic used was F-statistic which will be helpful in solving some problems in Chapters 10, 11 and 12.

We started the new Chapter 10 by first looking at a farming problem where the farmer is trying to determine whether she should use low, medium or high level of fertilizer to maximize the yield. To obtain samples we use experimental design with one factor.

The hypothesis that all levels of fertilizer are equally effective is tested using Analysis of Variance (ANOVA). We compare the between and within group variabilities which leads to a one-sided F-test. We found in the example that we can reject the equality hypothesis with a very low p value. We then looked at the confidence intervals for the differences between the means to see if one particular level of fertilization is better than the others. Chapter 10 ended by solving the same problem using MegaStat and examining the Summary Table which includes all the numbers we found manually.

In Week 11 we will do the course evaluations.

Summary for Week 10 (November 16-18)

We completed the discussion of Chapter 8 by considering a bottling problem (two-sided test) and then a problem with unknown population variance (which required us to use the t-distribution).

Chapter 9 was started with a problem involving the weight losses as a result of using the Atkins diet vs. the conventional diet. In this chapter we still make use of confidence intervals and hypothesis testing, but for two populations. Therefore, we don't encounter any new theory, but some of the formulas slightly differ from what we saw in Chapters 7 and 8. For example, when the variances are not known, we may assume their equality (which must be tested) and then compute the pooled variance.

The class ended by having two students toss 15 tennis balls into a bucket and testing the hypothesis that their success rates are equal. This material is not going to be in the final exam, but we did it to illustrate the use of MegaStat and to have some fun.

We will complete Chapter 9 in Week 11.

Posting of assignment and exam marks

Dear Bus Q600 students:

As you know, I have been posting your assignment and exam marks on the course web site as a .pdf file after removing your first and last names. The only information that remains on the .pdf file about you is your student number which you should not reveal to others.

If you are not comfortable with this method of reporting your marks, please let me know so I can remove all information from the .pdf file related to your student number and your marks.

Midterm exam results

We have finally sorted out the problems with missing/incomplete student numbers on the scan sheets. The exam marks can be accessed by clicking on this link.

The population mean is μ = 81%, which is very close to what I reported as the mean 79% of a sample of n = 5 exams. The distribution is bi-modal, meaning that there is a large number of marks around 80%, but also a bunching around 55%.

I am pleased with these results, but I hope that the students who had low marks will try harder in the final exam.

Summary for Week 9 (November 9-11)

I started by informing the class that the exams were still not completely marked because a few students entered their student numbers incorrectly on the scan sheets. This was taking us some time to sort out and that the results would be available early Week 10. However, a random sample of n = 5 exams which were marked manually revealed a sample mean of 79%, with a 95% CI ranging from 70% to 88%.

I then returned to the confidence interval problem for a proportion and talked about the election polls where interviewing roughly 1000 respondents is sufficient to get a 95% CI with a 3.1% margin of error. We found the correct sample size from a formula for n. This completed the discussion of Chapter 7.

Chapter 8 started with a taste test where a student claimed that he/she can tell the difference between Coke and Pepsi. The null hypothesis was that he/she would just be guessing. See this link for details of the experiment.

Null and alternative hypotheses were discussed in greater detail which were followed by a definition and examples of Type I and Type II errors. A one-sided test example with z-test involving cigarette tar content was presented. I then talked about the very important matter of p-value and showed that this value was very small in the cigarette example resulting in rejecting H0 for all α > p. The class ended with an example involving the DSB GMAT scores for 2005 (where the p value was very large, given the sample mean).