Special Review Exercises (p.105)—Except #4 and #11, which are scanned separately from these answers.
1. False. You don’t want test scores clustered around 50 with the A’s being outliers. Not all data sets follow the normal curve.
2. a) The SD of a list is 0. This means (ii) all the #’s on the list are the same…in other words, the spread is 0. Example: 5, 5, 5, 5 would have an average of 5 with the deviations from that average being 0 for all entries, so the SD = 0.
b) r.m.s. size of a list = 0; This means (iii) all the #’s on the list are 0. (The answer doesn’t = (iv) because…try -2, -1, 0, 1, 2, where the average is 0, but the r.m.s. would not be.)
3. You could use the first two with both the original and standard units to set up 2 equations using (entry - average)/ SD = standard units, to find the average and SD. But another way (maybe easier): Since 79 and 64 are one SD apart (1.8 - 0.8 = 1), we know that the SD = 15 original units. To find the average, use (entry - average)/ SD to get: (64 - ave)/15 = 0.8, so 64 - ave = 12, and 64 - 12 = ave. Since the average = 52, it’s standard unit form = 0. To find the last 2 blanks: (72 - 52)/15 = 1.3333 to go in the blank for the standard units. For the last blank, (entry - 52)/15 = -1.4, which gives (entry - 52) = -21, and the entry = 31.
4. See a separate scanned sheet…put with #11.
5. Human error.
6. a) Since there was an equal # of men and women, the average together = 625.
b) With men and women together, the spread would be larger, the SD would be larger and more than 125.
7. a) With 600 men out of 1000 people (400 women), the men are 600/1000 or 60% or 0.6 of the entire group. The women are 0.4 (or 40%) of the group. So to find the average, use: 0.6(650) + 0.4(600) = 390 + 240 = 630, the average of the men and women together.
b) SD would still be more than 125.
8. Too low. The curve is under the histogram for that interval.
9. The average # wrong is 3.6 with an SD of 2, since the # wrong = 10 - # right, with the same amount of spread.
10. False. This was not a longitudinal study. In the “olden days” people were pressured to be right handed.
11. See a separate scanned sheet…put with #4.
12. omit
13. a) As people get older, they are more prone to heart attacks.
b) You want to have as few pre-existing conditions as possible that might confound the study.
c) Drivers and conductors would likely be more similar in education, salaries, eating habits, etc.
d) This is an observational study…confounding is possible.
e) Weight excess can be hard on the heart. Were the drivers heavier than the conductors (in general) at the time they were hired—maybe that’s why they were hired for one position over the other? (As it turns out, in this study, that was the case—the drivers were heavier than the conductors hired.)
14. Yes, it would bias the study. The treatment group would have more people at risk than the control group, biasing against the treatment.
15. omit