AP Statistics / Mr. Hansen 11/19/2002; rev. 1/8/2007

Name: _________________________ Test #3

Test on §§4.1 through 5.2

Instructions are the same as always.

• No partial credit will be awarded in the multiple choice section. There is a penalty for guessing incorrectly.
• In the free-response portion, use standard mathematical notation—never calculator notation.
• Justify all steps.
• Work top to bottom, left to right, and write legibly.
• Mark with a single neat “X” any portion you wish to be ignored during grading. (Do not waste time with large erasures.)
• No questions will be taken once the test has started. If you believe you have found a misprint, answer the question to the best of your ability and indicate clearly what assumptions you are making in the problem in order to continue working.
• Time will end promptly at 30 minutes (45 minutes for extra-time students). No work after that time will be graded.
• You can miss some problems and still earn a high score.

	Part I: Multiple Choice. 2 pts. for each correct answer, ½ pt. penalty for each wrong guess, 0 pts. for each omission
1.	[Please see Barron’s How to Prepare for the AP Statistics Advanced Placement Exam, 3rd ed., Martin Sternstein, Ph.D., p. 476, #9.]
2.	[Please see Barron’s book, 3rd ed., p. 453, #35.]
3.	[Please see Barron’s book, 3rd ed., p. 454, #38.]
4.	[Please see Barron’s book, p. 481, #33.]
	Part II. Free Response. This section will be scored holistically (0-4 scale) and weighted as 2/3 of your score. (Note: On the real AP examination, the two sections will be weighted equally.)
5.	Read the following scenario and note at least four types of bias that are evident. Important: For each type of bias, list the standard name for that bias, a brief reason for how you know it will occur in this setting, and the direction of the bias (in other words, will this bias tend to increase or decrease the estimate of the population parameter?). If you find four solid types of bias, you will earn full credit; there is no need to make an exhaustive list. STA Lower School students and parents will be polled on their beliefs of how well the school is fulfilling its mission. For the Lower School students, the question will be worded as follows: “Do you enjoy attending St. Albans, and do you think the school is doing a good job overall?” For parents, the question will be worded as follows: “You concur, do you not, that St. Albans School is fulfilling to a significant degree the mission as set forth by the Board in the Long-Range Planning Statement, as revised?” Two surveys (one of each type) will be mailed to each Lower School family, and collection boxes will be set up in Mrs. DeBord’s office in Steuart 203. The parameters of interest are the percentages of each group (Lower School students and their parents) who answer “Yes” to the question posed.

6.

Briefly outline (diagrams and sentence fragments are acceptable) an experimental design that addresses the following research question: Does a 60-cycle electrical buzz in a classroom decrease students’ performance on a geometry quiz? Indicate briefly how the three elements of good experimental design are addressed by your design. If you use more than half of the page, you are probably writing way too much.

7.	A researcher notes the following relationship between annual income and happiness, where happiness is measured on a scientifically developed scale that takes a variety of factors into account.
	Income ($thousands)	Happiness index
	10	0.91
	20	0.94
	30	0.96
	40	0.99
	50	1.01
	60	1.04
	70	1.06
	80	1.08
	90	1.09
	100	1.11
(a)	Is a linear regression model, treating income as explanatory and happiness as response, appropriate for these data? Plot the data, and assess the r value and any other relevant indicators.
(b)	Another researcher proposes a shifted logarithmic model (i.e., response variable as a logarithm of a linear function of the explanatory variable). Explain why this conclusion is more intuitively appealing than a linear model.
(c)	Provide graphical and/or quantitative evidence to support a decision to consider a shifted logarithmic model. Do not actually compute the shifted logarithmic model just yet.
(d)	Now use an inverse transformation to find the appropriate shifted logarithmic model.
(e)	Show quantitative evidence to decide which model is superior, the linear regression model or the shifted logarithmic model. What do you conclude?
(f, g)	Estimate the happiness index value that is predicted for an annual income of $18,500, using both the linear model and the shifted logarithmic model. Show your work.
(h)	What income (approximately) is needed for a happiness index of 1.02? Describe briefly how you obtained this value, or if you could not, state why not. Full work is not required.
(i)	What income (approximately) is needed for a happiness index of 1.45? Describe briefly how you obtained this value, or if you could not, state why not. Full work is not required.