

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. 612 (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
XtoY 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. 613 (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 leastsquares 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 leastsquares line in Fig. 613 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 leastsquares 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. 614 (on page 220), the span most likely to produce "outcome X"
is the one in which the area of the shaded region between the bellshaped
curve and the independentvariable 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. 614. Therefore, we have no way of knowing which span of
independentvariable 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. 
