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 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