Math 143 C/E, Spring 2001
IPS Reading Questions
Chapter 7, Section 2 (pp. 537-548)



  1. The tests of significance of Sections 6.2 and 7.1 have both been for means (one type of sample statistic for quantitative data), and both can be classified as 1-sample procedures. In Section 7.2 we learn about 2-sample procedures (two-sample z and two-sample t). Why is this naming scheme (one vs. two sample) appropriate?








  2. Suppose that x1 and x2 are quantitative variables that come from populations known to be distributed as N(m1, s1) and N(m2, s2) respectively. What distribution should you expect for x2 - x1? How about for `x2 - `x1, where `x1 represents the mean value of x1 for a sample of n1 units taken from the first population, and `x2 is found similarly from a sample of n2 units taken from the second population?








  3. What would be the center of any level C confidence interval for the difference of means m2 - m1? Suppose the 95% confidence interval for this difference was (-1.75, -0.36). Which of the means m1 and m2 would you say (with 95%) is larger? Would you say the same if that 95% confidence interval were (-1.75, 0.61)?








  4. On p. 541 we receive the news that, when sample standard deviations replace population s. d.'s in the computation of a t statistic (instead of a z statistic), the resulting t statistic does not have a t distribution. Nevertheless we are told how to find a value of df (we will use method 2) so that this statistic is approximately distributed as t(df). At this point, the authors say that you can count on this approximation being conservative, a word that they have used before for approximate distributions (on p. 516). Just what does this word conservative mean for us?








  5. Notice how the paragraph on p. 545 that immediately follows Example 7.15 addresses concerns raised by the seven critical components of a study. Ideally, any study you read about in the news media would give information like this explaining some of the pitfalls of that type of study as well as how they were addressed whenever possible by the researcher. (Note: There is no question posed here.)

  6. Under what conditions are the results of the two-sample procedures most trustworthy?