PLCY 610 HW #1
1. Do the following questions from the text: 1.160, 1.164, 1.176
a. 1.160: Visit the webpage http://www.statcan.gc.ca/tables-tableaux/sum-
som/l01/cst01/econ01a-eng.htm that provides data on Canada’s balance of
international payments. Select some data from this webpage and use the methods
learned in chapter 1 to create graphical and numerical summaries. Write a report (one
page maximum) summarizing your findings and that includes supporting evidence from
your analyses.
b. 1.164: Below are data on park and open space in several U.S. cities with high population
density. In this table, population figures are reported in thousands of people, and park
and open space is called open space, with units in acres.
C i t y Po p u l a t i o n O p e n S p a c e
B a l t i mo r e 651 5091
B o s t o n 589 4865
Ch i c a g o 2896 11645
L o n g B e a c h 462 2887
L o s A n g e l e s 3695 29801
M i a mi 362 1329
M i n n e a p o l i s 383 5694
N e w Y o r k 8008 49854
O a k l a n d 399 3712
P h i l a d e l p h i a 1518 10685
S a n F r a n c i s c o 777 5916
W a s h i n g t o n D C 572 7504
(a) Make a bar graph for population. Describe what you see in the graph.
(b) Do the same for open space.
(c) For each city, divide the open space by population. This gives rates: acres of
open space per thousand residents.
(d) Make a bar graph of the rates.
(e) Redo the bar graph that you made in part (d) by ordering the cities by their
open space to population rate.
(f) Which of the two graphs in (d) and (e) do you prefer? Give reasons for your
answer.
c. 1.176: Raw scores on behavioral tests are often transformed for easier comparison. A
test of reading ability has mean 70 and standard deviation 10 when given to third-
graders. Sixth-graders have mean score 80 and standard deviation 11 on the same test.
To provide separate “norms” for each grade, we want scores in each grade to have
mean 100 and standard deviation 20.
(a) What linear transformation will change third-grade scores x into new scores
xNEW = a +bx that have the desired mean and standard deviation? (Use b > 0
to preserve the order of the scores.)
(b) Do the same for the sixth-grade scores.
(c) David is a third-grade student who scores 72 on the test. Find David’s
transformed score. Nancy is a sixth-grade student who scores 78. What is her
transformed score? Who scores higher within his or her grade?
(d) Suppose that the distribution of scores in each grade is Normal. Then both
sets of transformed scores have the N(100, 20) distribution. What percent of
third graders scores less than 75? What percent of the sixth-graders scores
less than 75?