Statistics Demystified, 2nd edition Stan Gibilisco Explanations for Quiz Answers in Chapter 1 1. Whenever we plot a two-dimensional graph that portrays a function of a variable quantity (in this case time), then we can define that quantity as the independent variable. The correct choice is C. 2. By definition, a rational number is a quantity that we can express as an integer divided by a positive integer. Rational numbers can appear as ratios of whole numbers (although in that case we'll always get a positive value), so choice A makes this statement true. When we write a rational number in decimal form, we sometimes get endless repeating sequences of numbers after the decimal point, so choice B works here. All even integers are rational numbers "by default," because they're ratios of themselves to 1, which is a positive integer. Choice C works as well. The answer is therefore D, "All of the above." 3. In Fig. 1-20 on page 36, point R belongs to set A and also to set C, but not to set B. Therefore, point R belongs to the intersection of sets A and C; we write that fact asR ∈ A ∩ C Choice is D provides a valid answer. However, choice C also works! Because R ∈ A, we know that point R belongs to the union of set A and any other set, including set B. We can correctly say that R ∈ A ∪ B We can answer either C or D to this question. 4. In Fig. 1-20, point U belongs to set A and also to set B, but not to set C. The correct choice is B, which we can write symbolically asU ∈ A ∪ B We can rule out choices A, C, and D straightaway because they all specify intersections of set C with something else; when we look at the diagram, we can see clearly that U ∉ C (point U is not an element of set C). 5. In Fig. 1-20, point T does not belong to any of the three sets A, B, or C. Therefore, T is not an element of the union of those three sets, a fact that we can write symbolically asT ∉ (A ∪ B) ∪ C The correct choice is C. 6. In a vertical bar graph, the bars run "the long way" vertically up and down. The heights of the bars portray the values of the dependent variable. We plot the independent variable along the horizontal axis, and we plot the dependent variable along the vertical axis. The correct choice is B. 7. We can reasonably expect that as the temperature rises above freezing, snow will become less likely, and as the temperature falls below freezing, snow will become more likely (if all other factors remain constant). The correct choice is A. The "snowiness" of a climate correlates negatively with rising temperature, but positively with the frequency of storms, and positively with the number of observed polar bears (again, if all other factors remain constant!). 8. When we try to predict future events or trends based on past or current information, we extrapolate. The simplest method is linear extrapolation. The correct choice is A. 9. A function is a special form of relation. Therefore, choice B holds true all the time. Choices A and C do not always hold true, and choice D is absolutely false! 10. In a nondecreasing function, the value of the dependent variable can never get smaller as the value of the independent variable grows larger. The value of the dependent variable can remain constant or increase (or both, at intervals) as the value of the independent variable goes up. The correct choice is A.