Practice Assignment (to be discussed randomly Wednesday, April 21)

1) A single test at the a=.05 level will wrongly reject H₀ only 5% of the time when H₀ is actually true. In class, we discussed making three separate tests at the a=.05 level. Explain why we expect to be wrong for at least one of the three tests more than 5% of the time.

2) The following two-way table classifies hypothetical hospital patients according to the hospital that treated them and whether they survived or died:

(a) Which hospital saved the higher percentage of its patients? How would you test if there was a significant difference in the survival rates at the two hospitals?

Now we categorize each patient according to whether they were in fair or poor condition prior to treatment:

(b) Among those if fair condition, compare the recovery rates for the two hospitals. Which hospital saved the greater percentage?

(c) Among those in poor condition, compare the recovery rates for the two hospitals. Which hospital saved the greater percentage?

(d) Explain how it happens that hospital B has the higher recovery rate overall, yet hospital A has the higher recovery rate for each type of patient?

(e) Which hospital would you rather go to if you were ill? Explain.

3) A population paperback book is published in a choice of four different covers. A certain bookstore keeps copies of each cover on its racks. To test the hypothesis that sales are equally divided among the four choices, a random sample of 100 purchases is identified.

(a) If the results C² value is 6.4, what conclusion would you reach when using a test with significance level .05?

(b) What conclusion would be appropriate at significance level .01 if C²=15.3?

(c) If there were six different covers rather than just four, what would you conclude if C²=13.7 and a test with a=.05 is used?

Homework Assignment (Due Friday, April 23)

1) (p. 652) 9.22 Give numerical and graphical summaries and perform the appropriate test of significance, (p. 654) 9.30

2) Construct your own hypothetical data to illustrate Simpson’s paradox in the following context: Show that it is possible for one softball player (Amy) to have a higher percentage of hits than another (Barb) in the first half of the season and in the second half of the season, and yet have a lower percentage of hits for the season as a whole. I’ll get you started: suppose that Amy has 400 at-bats in the first half of the season and 100 in the second half, and suppose that Barb has 100 at-bats in the first half and 400 in the second half. This creates an inequity in sample size. You are to make up how many hits each player had in each half of the season, so that the above statement holds (the proportion of hits is the number of hits divided by the number of at bats).

3) (p. 781) 12.8, 12.22