Partial Answer Key to Test #2

AP Statistics / Mr. Hansen
10/20/2004 [rev. 11/9/2004]

Name: _________________________

Note: This answer key is provided in order to help you check a few of the answers from the October 1998 test. Some of the details are omitted here. Remember that you must show full work for full credit. In general, full work consists of formula, plug-ins, and answer (circled, with correct units such as dollars or years).

2.	response variable

3.	statistics

4.	parameters

5.	matched pairs

11.	b₁ = rs_y/s_x = (–.9044335)(.35/.28) = –1.1305

12.	(a) No change. [The formula for r treats x and y symmetrically; r is not affected by a switch.]
	(b) b₁ = rs_y/s_x = (–.9044335)(.28/.35) = –.72355, where s_y = old s_x, and s_x = old s_y

13.	No. First, there could be clustering patterns that conspire to give an overall r value near 0. Second, there could be a strong nonlinear association. A sinusoidal association, a parabolic association, or a V-shaped association are but a few in the vast collection of nonlinear associations that could easily yield an r value close to 0.

14.	A cause-and-effect link is not required. As long as the r value is close to 1 or –1, and as long as you are not trying to work with x values that are to the left or right of the values for which plentiful data exist, using the LSRL for prediction is quite safe and is done all the time in the real world. When people try to use the LSRL to make predictions involving x values that are to the left or right of the values for which plentiful data exist, they are committing a reasoning fallacy known as extrapolation.

15.	(a)
	(b) The fact that smoking incidence has declined in each age group strongly suggests, to a layperson, that the overall incidence of underage smoking has declined. However, since the problem stated that the overall incidence of smoking for people under age 18 has increased, Simpson’s Paradox must be at work. The lurking variable is most likely the demographic makeup of the communities in which BTC has placed billboards. If there has been a large shift from pre-teens to teenagers in the past year, either through immigration or the mere aging of a large 12-year-old cohort, then the weighted average incidence of smoking could well have increased from 13% last year to 15% this year. Note that this would require that pre-teens were a majority of the under-18 crowd last year, while teenagers are a majority of the under-18 crowd this year.