Solutions for Session 7, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6| C7| C8| C9| C10| C11

 Problem C1 Even though we have established an association, we have not established a description of the nature of the relationship between height and arm span. This question seeks to investigate a specific relationship between arm span and height. Put another way, there are many positive associations (e.g., the association between years of job experience and salary), but the relationship between the variables is not that they are the same (i.e., "square").

 Problem C2 Answers will vary, but you should generally find the heights and arm spans to be approximately the same.

Problem C3

 a. It tells you that this person's height is greater than his or her arm span, and that this person is not "square." It does not tell you the person's exact height or arm span. b. It tells you that this person's height is less than his or her arm span, and that this person is not "square." Again, it does not tell you this person's exact height or arm span. c. It tells you that this person's height and arm span are equal, and that this person is "square."

Problem C4

 a. Two of the five people, Persons 1 and 6, have heights that are greater than their arm spans. b. Two of the five people, Persons 14 and 19, have heights that are less than their arm spans. c. Person 19 has the largest difference, 6 cm. d. Person 9 has the smallest difference, 0 cm. Person 9 is "square."

Problem C5

 a. Nine people have heights that are greater than their arm spans. b. Twelve people have heights that are less than their arm spans. c. Three people have heights that are equal to their arm spans. d. Persons 5, 6, 8, 14, 18, and 22 -- the six people with the smallest non-zero difference (±1) in their heights and arm spans -- come the closest to being a square without actually being a square. e. Persons 24, 23, 11, 7, and 20 -- the people with the greatest difference (positive or negative) between their heights and arm spans -- are the most "non-square."

Problem C6

 a. Five people have heights and arm spans that differ by more than 6 cm. b. Nine people have heights and arm spans that differ by less than 3 cm.

Problem C7

 a. Person 1's height is greater than his or her arm span, so the coordinates of that point will be above the line Height = Arm Span. b. Person 9's height is equal to his or her arm span, so the coordinates of that point will be on the line Height = Arm Span. c. Person 19's height is less than his or her arm span, so the coordinates of that point will be below the line Height = Arm Span. d. Any point on the line Height = Arm Span represents a person who is "square." Any points that are not on this line would indicate that a person's height is either greater or less than that person's arm span.

 Problem C8 Since the difference between height and arm span is greater for Person 1 than it is for Person 6, the point for Person 1 should be farther from the line Height = Arm Span than the point for Person 6.

 Problem C9 The vertical distance for Person 14 is 1 (|176 - 177| = |-1| = 1). The vertical distance for Person 19 is 6 (|182 - 188| = |-6| = 6). In each case the calculation is performed as |Height - Arm Span|.

Problem C10

 a. The points for Persons 2 and 7 are above the line; therefore, their heights are greater than their arm spans. b. The points for Persons 4 and 23 are below the line; therefore, their heights are less than their arm spans. c. The point for Person 23 is the farthest from the line, vertically; therefore, Person 23 has the greatest difference between height and arm span. d. The point for Person 2 is closest to the line, vertically; therefore, Person 2 has the smallest difference between height and arm span.

Problem C11

 a. Nine points are above the line, so nine people have heights that are greater than their arm spans. b. Twelve points are below the line, so 12 people have heights that are less than their arm spans. c. Three points are on the line, so three people have heights that are equal to their arm spans. d. The points that are farthest from the line represent people who have the greatest differences between heights and arm spans. (These are the points for Persons 11, 23, and 24.) e. The six points that are closest to the line represent the smallest differences between heights and arm spans. (These are the points for Persons 5, 6, 8, 14, 18, and 22.)

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