The full quiz is here. The answers appear below. Comments, which are not part of the answers, are italicized.
1. Sketch a Q-Q plot showing a batch that has longer tails (high and low) than the reference distribution.
2. Sketch a Q-Q plot where half of the batch consists of nondetects, all with the same detection limit. Assume all the detected values are above the detection limit.
3. Sketch a Q-Q plot where the reference distribution has a single mode and the batch has two widely separated modes.
The two separated modes will cause the quantiles to increase slowly near the modes and very rapidly between the modes. The plot will therefore be S-shaped.
4. Sketch a Q-Q plot, as accurately as possible (show scales on the axes), where the batch has a shape essentially identical to the reference distribution but has twice the spread.
The slope must be about two.
5. Sketch a Q-Q plot, as accurately as possible (show values on the axes), where the batch differs from the reference distribution only in location.
The slope must be about one, but the intercept must be distinctly nonzero.
6. Sketch a Q-Q plot where the batch is essentially identical to the reference distribution but has two high outlying values.
7. Sketch a plot that consists of a curve in the X-Y plane but that cannot be a Q-Q plot for any possible set of data.
A Q-Q plot must be monotonic.
8. Ln(2) = 0.7 and Ln(5) = 1.6
(approximately). Compute (to one decimal place), showing your work:
a) ln(10) = ln(2 * 5) = ln(2) + ln(5) =
2.3
b) ln(40) = ln(23 * 5) =
3*ln(2) + ln(5) = 3.7
c) log2(5) = ln(5) / ln(2) =
2.3
d) ln(0.5) = ln(1/2) = -ln(2) = -0.7
e) exp(ln(2)) = 2, by definition.
This answer is exact.
Scoring: The passing score is 96.
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This page was created 26 January 2001.