AP Statistics / Mr. Hansen	Name: __________________________
10/1/2014	Battery bonus (for Mr. Hansen’s use only): ____

Test #1

If your calculator fails during the test, do the best you can without it. There is no sharing of calculators, batteries, or other supplies during the test. RAISE YOUR HAND if you have a question. No talking.

Answer each question in a way that reveals that you know what you are talking about. Complete sentences are not required unless specified. However, spelling and grammar do count for points.
1. (6)	(a) Explain why the proportion of heads in 4500 flips (the “sample proportion of successes”) of a certain coin is a statistic, but the probability that the coin shows “heads” when flipped is not. ________________________________________________________________________ ________________________________________________________________________ (b) What do we call the probability that the coin is heads, if not a “statistic”? _______________
2. (4)	What symbol do Mr. Hansen and the AP question writers use for the probability referred to in question 1? _____ Does your textbook use the same notation (write “Yes” or “No”)? _____
3. (9)	In addition to computing statistics, which can certainly be useful, there is something that Mr. Hansen stressed and stressed that you must always do in our class. Hint: Examples of implementing this advice include boxplots, modified boxplots, scatterplots, and/or histograms. “_________________________________________________________________________ !”
4. (4)	(a) What information does a time series plot show that a histogram does not? ________________________________________________________________________ (b) Dotplots, histograms, and ____________ all give a sense of the distribution (shape) of data.
5. (6)	(a) Both bar graphs and pie graphs can be used to show the relative counts of _______________ data from a data set. (b) Which type of graph (bar or pie) is more useful when the objective is to show the contribution of each category to the whole? __________ (Note: This is usually not what people need to know.) (c) Which type of graph (bar or pie) is more useful when the objective is to compare the relative sizes of the categories? __________ (Note: This is usually what people, especially businesspeople, care about. If they request the other type of graph, they may not be asking for what they need.)
6. (6)	Most distributions from banking, finance, and economics are skew ____________ . In other words, the mean is noticeably ____________ than the median.
7. (6)	Most distributions from the natural world have a specific bell shape known as the ____________ shape or are at least mound-shaped. ____________ distributions are sometimes seen if the males and females of a species are combined into the same distribution, but most distributions of natural data (height, weight, IQ, etc.) have only one peak and are therefore called unimodal.
8. (5)	In order to prove a cause-and-effect relationship between two variables, whether they be categorical or quantitative, it is necessary to _________________________________________ .
9.	Here is a data set showing the relationship between homework level and whininess for a sample of Lower Schoolers:
		HW (hrs. per night)	Whininess (decibels)
		0.5	93
		0.75	91
		0.8	92
		1.1	88
		1.1	87
		1.25	81
		1.5	83
		1.8	81
		2	83
		2.2	78
		2.3	77
		2.3	76
		2.5	71
		2.5	78
		2.5	76
		2.5	76
		2.5	75
(10)	(a) Compute the 5-number summary for each column: HW (hrs./night): ____ , ____ , ____ , ____ , ____ Whininess (dB): ____ , ____ , ____ , ____ , ____
(4)	(b) Compute the sample mean of HW hours per night, and write an equation using proper notation.
	____ = ____
(4)	(c) Compute the sample s.d. of whininess, and write an equation using proper notation.
	____ = ____
(4)	(d) Use your calculator to create a histogram of whininess, using a bin size of 5 dB. Raise your hand in order to earn these points. Mr. Hansen’s use only: _________
(6)	(e) Comment on the distribution seen in part (d). The AP exam requires three aspects of the distribution for full credit. If you can’t remember all three, simply comment on what you see. ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________
(6)	(f) On the back of page 1, make a scatterplot with HW on the x-axis and whininess on the y-axis. Exactness is not required. For full credit, mark your axes with the three features discussed in class.
(3)	(g) Is the association between HW and whininess positive or negative? _________
(4)	(h) Explain what your answer to (g) means in the context of this problem. Note: Explaining “in context” means that you must use the words “homework” and “whininess” in your answer. It is perfectly acceptable to abbreviate “homework” as “HW.” ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________
(2)	(i) Estimate the whininess of a Lower Schooler who has 1.0 hours of nightly homework. No work is expected, and you are not expected to run a linear regression, since we have not yet reviewed that topic from precalculus. However, your answer must include units for full credit. ________________
(1)	(j) Does more HW cause a reduction in whininess? (Write “Yes,” “No,” or “Insufficient information.”) _________
(1)	(k) Does more whininess cause a reduction in HW? (Write “Yes,” “No,” or “Insufficient information.”) _________
(1)	(l) Is HW level useful for predicting whininess? (Write “Yes,” “No,” or “Insufficient information.”) _________
(1)	(m) Is whininess useful for predicting HW level? (Write “Yes,” “No,” or “Insufficient information.”) _________
(4)	(n) Write the symbol for the true variance of whininess for all possible Lower Schoolers, not the variance computed from this sample: _____ . What are the units of this quantity? ___________
(6)	(o) Fill in the blanks. The data set given at the beginning of the problem (n = ______ ) is probably a sample drawn from a single teacher’s class, i.e., a _____________________ sample. Describe how we could obtain a true SRS of Lower School students. ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________