STAtistics / Mr. Hansen

2/11/2011

Condensed Chapter Summary for Chapter 11

Dear Students:

    Your textbook’s Chapter 11 summary on pp. 633-634 contains some extraneous material. In my continuing quest to improve your learning experience, I offer here my condensed version of a chapter summary, with only 8 entries instead of 14. Please let me know if you see anything missing or if anything is unclear.

Independent samples	Two samples that either come from separate populations or, if they come from the same population, have no links between them. For example, if 300 medical research subjects are randomly divided into a control group and an experimental group, we would say the samples are independent even though they were drawn from the same initial population. Independent samples often have slightly different sample sizes, which is a giveaway clue.
Paired samples	Two samples for which each observation in one sample is paired in a meaningful way with a corresponding observation in the other sample. We treat paired samples as if they were a single sample of the differences, and we would use 1-sample t or 1-prop. z procedures. It is wrong to use 2-sample procedures when the samples are paired.
	The t test statistic for means or differences of means is always computed the same way. The s.e. in the denominator must be selected from the appropriate box on the AP formula sheet.
	Formula for constructing a confidence interval for a mean (or difference of means). The s.e. must be selected from the appropriate box on the AP formula sheet.
df = [big mess]	The degrees of freedom for a 2-sample t situation will always be computed by software! It is only in the 1-sample (or matched pairs) case that df = n − 1.
	Here, pc is the statistic for estimating the common population proportion when p1 = p2. This formula occurs in a 2-prop. z test situation where we have H0: p1 = p2. Confusingly, the AP formula sheet calls this value p instead of pc and does not provide the formula shown at left because it is considered “obvious.” (It is simply a weighted average.) If you find this to be confusing, then ignore it and let the calculator compute it for you.
	The z test statistic for proportions or differences of proportions is always computed the same way. The s.e. in the denominator must be selected from the appropriate box on the AP formula sheet. Note that “hyp. value” is often 0.
	Formula for constructing a confidence interval for a proportion (or difference of proportions). The s.e. must be selected from the appropriate box on the AP formula sheet.