AMS 5 Practice 8
Chapter 10, #1, 2, 3, 5, 7, 9
1. Shown below is a scatter diagram for Math and Verbal SAT scores for graduating seniors
at a certain high school. Three areas are shaded. Match the area with the description.
(One description will be left over.)
(i) Total score (Math + Verbal) is below 800
(ii) Total score (Math + Verbal) is around 800
(iii) Math score is about equal to Verbal score.
(iv) Math score is less than Verbal score.
2. In a study of the stability of IQ scores, a large group of individuals is tested once at age
18 and again at age 35. The following results are obtained.
age 18: average score ~ 100, SD ~ 15
age 35: average score ~ 100, SD ~ 15, r ~ 0.80
(a) Estimate the average score at age 35 for all the individuals who scored 115
at age 18. (b) Predict the score at age 35 for an individual who scored 115 at age 18.
2a) Guess: 112 (15*.8 = 12)
2b) 15/15 = 1 .8*1 = .8 .8*15 + 100 = 112
3. Pearson and Lee obtained the following results in a study of about 1,000 families:
Average height of husband ~ 68 in, SD ~ 2.7 in
Average height of wife ~ 63 in, SD ~ 2.5 in, r ~ 0.25
Predict the height of a wife when the height of her husband is
(a) 72 in (b) 64 in (c) 68 in (d) unknown
3a) 4/2.7 = 1.48 .25*1.48 = .370 .370*2.5 + 63 = 63.9259 in
3b) -4/2.7 = -1.48 .25*-1.48 = -.370 -.370*2.5 + 63 = 62.0740 in
3c) 0/2.7 = 0 .25*0 = 0 0*2.5 + 63 = 63 in.
3d) 63 + (unknown/2.7*.25*2.5) ~ 63% - it’s in the middle
5. An investigator measuring various characteristics of a large group of athletes found that
the correlation between the weight of an athlete and the amount of weight that athlete
could lift was 0.60. True or false, and explain:
(a) On the average, an athlete can lift 60% of his body weight.
(b) If an athlete gains 10 pounds, he can expect to lift an additional 6 pounds.
(c) The more an athlete weighs, on the average the more he can lift.
(d) The more an athlete can lift, on the average the more he weighs.
(e) 60% of an athlete’s lifting ability can be attributed to his weight alone.
5a) False; the r doesn’t specify how much the athlete can lift, only that it’s related to body
5b) False; see above reason.
5c) True; there is a correlation based on the data
5d) True; there is a correlation based on the data
5e) False; see 5a) and 5b) reasons, also there’s no differentiation between fat weight and
muscle weight. 7. A doctor is in the habit of measuring blood pressures twice. She notices that patients who
are unusually high on the first reading tend to