Statistics Demystified, 2nd edition

Stan Gibilisco

Explanations for Quiz Answers in Chapter 6

1. When we want to get a good view of the nature and extent of the correlation (if any) between two variables, we can record individual data points on a coordinate grid called a scatter graph or scatter plot. The correct choice is D.

2. By nature, an alternative hypothesis involves an assumption to the effect that the main (null) hypothesis is false. The answer is B.

3. In Fig. 6-12 (on page 218), the points are arranged in an obvious pattern, but not in a way that shows correlation. A positive correlation would appear as a tendency for the points to lie near a line that ramps upward as we go to the right. A negative correlation would appear as a tendency for the points to lie near a line that ramps downward as we go to the right. The points in this plot, while making a neat picture, don't cluster themselves near any particular line, so the X-to-Y correlation is near or equal to 0. The correct choice is A.

4. We want to get an idea of the extent of the correlation (if any) between two variables, and we have a large number of data points (365 of them, to be exact). A scatter plot will work best for this purpose. If we didn't have so many data points, a bar graph would also reveal correlation fairly well, but not as well as a scatter plot would do. The correct choice is B.

5. If we move the point at the extreme upper left in Fig. 6-13 (on page 219) from W = 1.5 and Z = 8.4 to W = 1.5 and Z = 6.1, we move the point straight downward by 2.3 units. That action will give us a least-squares line that ramps downward as we move to the right, in the same sense as before. But the line will slant a little less steeply than it originally did. The correct choice is A.

6. The least-squares line in Fig. 6-13 clearly ramps downward as we move toward the right. The value of W increases as we move toward the right, and the value of Z increases as we move upward. Therefore, by definition, the line has negative slope. The correct choice is A.

7. Because the least-squares line ramps downward, we know that the correlation is negative. Because the points appear clustered almost right along the line, we know that the correlation is strong, almost as strong as it can get. Therefore, the correlation is close to -1 (which would represent the strongest possible negative correlation). The correct choice is C.

8. In Fig. 6-14 (on page 220), the span most likely to produce "outcome X" is the one in which the area of the shaded region between the bell-shaped curve and the independent-variable axis is the largest. We can easily see that it must be span C, because all the spans have equal width. The answer is C.

9. We aren't given any quantitative increments for either graph axis in Fig. 6-14. Therefore, we have no way of knowing which span of independent-variable values approximates any particular probability that we'll observe "outcome X." The correct choice is D.

10. When we draw a conclusion based on the recorded results of experiments, we infer that conclusion, and we call the process inference. The answer is A.