Quest through p. 276, Version 3

AP Statistics / Mr. Hansen	Name: _______________________________________
11/10/2006

Quest through p. 276 in text, Version 3

Please read: Calculator and a handwritten note sheet are permitted. Point values: 2 pts. each for “matching” section, 4 points everywhere else. There is no penalty for wrong guesses (unlike on the AP exam, where each wrong guess costs 125% of the question’s value). MARK ANSWERS ONLY ON YOUR BUBBLE SHEET.

1.	In a linear regression, your calculator reports r² = 0.841. Which of the following is a true statement?
	(A) Approximately 84% of the variation in y can be explained by the variation in x. (B) Approximately 84% of the variation in log y can be explained by the variation in x. (C) Approximately 91.7% of the variation in y can be explained by the variation in x. (D) Approximately 91.7% of the variation in log y can be explained by the variation in x. (E) Approximately 70.7% of the variation in y can be explained by the variation in x.

2.	We store our x values in L₁ and our y values in L₂. We then compute a LSRL with STAT CALC 8 L₁,L₂,Y₁ to obtain r = –0.118. The residual plot shows no patterns. What happens if we re-run the LSRL, except this time using the command STAT CALC 8 L₂,L₁,Y₁?
	(A) r = –0.118, showing weak negative linear association between the variables (B) r = 0.118, showing weak positive linear association (since x and y were switched) (C) r = –0.118, showing strong negative linear association between the variables (D) r = 0.118, showing strong positive linear association (since x and y were switched) (E) [insufficient information to answer]

3.	A scatterplot shows an almost perfect linear relationship between x and y. The r² value is close to 1, and the residual plot shows no patterns. Can we infer that a change in y causes a change in x?
	(A) No, since it is more likely (statistically speaking) that a change in x causes a change in y. (B) No, unless x represents the control group in a controlled experiment. (C) No, unless y represents the control group in a controlled experiment. (D) No, since both x and y could be affected by a lurking variable. (E) Yes.

4.	Radio call-in shows, as a means of gauging public opinion in D.C., suffer primarily from . . .
	(A) response bias (B) voluntary response bias (C) undercoverage, since few people have access to radios		(D) placebo effect (E) overcoverage, since people with multiple radios in their house will hear the broadcast more than once

5.	What sort of person would you hire to design a push poll?
	(A) “spin doctor” (p.r. expert/political consultant) (B) moron (C) mathematician			(D) applied mathematician (E) statistician

6.	What topic has Mr. Hansen stressed more than any other?
	(A) bias (B) margin of error (C) cause and effect		(D) P value (E) conflict of interest

7.	In order to prove cause and effect by means of statistics, we need a number of ingredients. Which of the following ingredients is not required, however?
	(A) controlled experiment (B) hypothesis made before data are gathered (C) very large sample size		(D) methodology (E) statistically significant results supporting the hypothesis

8.	In the Nov. 7 “Quick Study” column, one of the studies involved stroke victims and alternative therapies to help them improve the use of their affected hand. Give a possible source of bias for this study.
	(A) no control group (B) lack of blinding (C) study was not an experiment		(D) treatments were not assigned randomly (E) sample size (222) was not nearly large enough

9.	In the Nov. 7 “Quick Study” column, one of the studies looked at possible associations between diet and cognitive decline in older people. What were the conclusions?
	(A) No association between diet and rate of cognitive decline was found. (B) Vegetable consumption and fruit consumption both cause a reduction in cognitive decline rate. (C) Vegetable consumption, but not fruit consumption, causes a reduction in cognitive decline rate. (D) Vegetable and fruit consumption are both associated with a reduction in cognitive decline rate. (E) Vegetable consumption, but not fruit consumption, is associated with a reduction in cognitive decline rate.

	In questions 10 through 12, suppose that “Chris,” a medical researcher, wishes to find publishable cause-and-effect relationships in order to impress a tenure review committee. Chris decides to perform 450 experiments all at once, using highly efficient microassay technology in a controlled experimental setting. (This is actually possible nowadays.) Chris’s plan is to publish and claim that cause and effect was proved statistically for each of the experiments in which the P value is less than 0.05. Recall that the P value, which is computed either by software or by calculator, is the probability that differences of a certain size (or greater) would occur, given that chance alone was the only force at work.

	To put this in plain English, Chris will publish and claim a cause and effect relationship for each experiment in which chance alone would cause such a striking outcome only about 1 time in 20.

10.	If chance alone were the only force at work, approximately how many of Chris’s 450 experiments will be “publishable” under this rather twisted concept of publishability? (Remember, Chris intends to publish each result where the P value is less than 0.05.)
	(A) 0 (B) 3 (C) 10		(D) 20 (E) 40

11.	Why is Chris’s concept of publishability unacceptable?
	(A) Chris’s laboratory provides no opportunity for a controlled experimental setting. (B) Microassay technology is too new to be used in experiments. (C) Since the hypotheses were not made before the experiments were run, the results are bogus. Chance alone can explain the fact that some of the experiments were successful. Unless Chris can predict which of the 450 experiments will show statistically significant results, there is nothing publishable here. Chris’s process is like a “witch hunt” for cause and effect. (D) Cause and effect cannot be proved statistically. (E) All of the above.

12.	Why is the legendary story of the “called shot” by Babe Ruth (famous U.S. baseball player, 1895-1948) relevant to our study of statistics?
	(A) Home runs occur nearly every day during the season, but a called shot would be an amazing thing indeed. No ordinary hitter could ever hope to point to a place in the bleachers and then hit a home run to that place. Chance alone could not plausibly explain such an occurrence. (B) Baseball fans are obsessed with statistics, perhaps more so than fans of any other sport. (C) The Curtiss Candy Company claimed that the Baby Ruth bar was not named for Babe Ruth. (D) The called shot allegedly occurred in the 1932 World Series at Chicago’s Wrigley Field, not far from where a certain statistics teacher used to visit on occasion in the 1980s. (E) The story is interesting but completely irrelevant.

13.	Although this type of bias can be involved in a variety of studies, it is an especially difficult challenge for surveys involving sensitive topics (e.g., drug use).
	(A) voluntary response bias (B) response bias (C) nonresponse bias		(D) bias caused by placebo effect (E) overcoverage bias

	Matching I. On your bubble sheet, mark the letter of the entry from the right column that best matches the numbered entry on the left. Each choice is used exactly once.

	___ 14. r	(A) response value (predicted by model)
	___ 15. r²	(B) response value (actual data)
	___ 16. b	(C) coefficient of determination
	___ 17. y	(D) true value of slope parameter in LSRL model of form a + bx
	___ 18.	(E) linear correlation coefficient

	Matching II. Same rules as above. Note that no entries are shared between lists. That is, questions 14-18 use choices A through E above, and questions 19-22 use choices A through D below.

	___ 19. s ___ 20. s² ___ 21. s² ___ 22. 0	(A) sample standard deviation (B) mean residual value in LSRL model (C) mean squared error, i.e., mean squared deviation from population mean (D) sample variance