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# Briefly describe the shape (modality and skewness) of the distribution of U.S. personal annual income.

INSTRUCTIONS TO CANDIDATES

1. The distribution of U.S. personal annual income in 1993 is as shown *:

* Found on http://www.gumption.org/1993/memo/landmarks/us_income.gif

1 (a) [8pts] Briefly describe the shape (modality and skewness) of the distribution of U.S. personal annual income.

1 (b) [5pts] Based on the shape of the distribution of personal income shown above, do you expect the mean to be greater than the median, less than the median, or equal to the median? [Hint, see lecture 3.]

[exercise 1 continues]

1 (c) [5pts] Based on the display on the previous page, which one of the following is the most reasonable value of the median U.S. personal annual income in 1993? [Hint, no calculation is necessary]

\$ 7 thousand

\$ 10 thousand

\$ 22 thousand

\$ 27 thousand

\$ 40 thousand

1 (d) [5pts] Based on the display on the previous page, which one of the following is the most reasonable value of the mean U.S. personal annual income in 1993? [Hint, no calculation is necessary]

\$ 7 thousand

\$ 10 thousand

\$ 22 thousand

\$ 27 thousand

\$ 40 thousand

2. Statistical analysis of ancient artifacts can help determine whether different village groups had contact with each other In one actual archeological excavation of ancient stone tools at two different sites (‘A’ and ‘B’) in Mesa Verde, Colorado, the stone composition of various tools was determined*.

* Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Bunt Mesa Pueblo and Casa del Rito, T. A. Kohler editor.

The stone artifacts were primarily of two different compositions (basalt or chert). The contingency table of counts of artifacts found at the sites is given:

location

Site A Site B

Basalt 806 543 1349

Chert 434 565 999

1240 1108 2348

Answer the corresponding questions on the following page:

[exercise 2 continues on next page]

The primary question of interest is whether composition differs by location (i.e., whether location predicts composition). In that case:

2 (a) [4pts] Between ‘composition’ and ‘location,’ which variable is the explanatory and which variable is the

response? [Hint, see lecture 5.]

2 (b) [4pts] Which one of the following will be most appropriate from the table for investigating the question of interest: Row conditional proportions; column conditional proportions; joint proportions; marginal proportions; or the raw counts? [Hint, see lecture 5, and take into account your previous answer and the layout of the table.]

2 (c) [8pts] Report the appropriate values for deciding whether location predicts composition (you can use a calculator).

2 (d)      [5pts] Is there evidence of a relationship in the study between location and composition? Briefly say how you know.

3. For each plot below, give the most reasonable correlation coefficient from the set of values here (note, some values won’t be used): –1.0, –0.97, –0.58, 0.01, 0.70, 1.0

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