AP Statistics / Mr. Hansen	Name: _______________________________________
1/30/2007

Test on Chapters 7, 8, and Beginning of 9

• Calculator is OK throughout.
• If a blank is provided, give the short answer that fits best.
• If a gap is provided, provide adequate justification/explanation, and circle your answer.
• In #9, 10, and 11, work was optional during the administration of the test, but now, you should show all of your work.

1.	State the definition of “sampling distribution.” ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________
2.	Two statistics students are arguing about their methodologies. One of them says, “Your methodology uses an SRS to estimate the sample mean, which means you’re guaranteed to have bias.” The other retorts, “Oh, yeah? Well, my methodology may have bias, but at least it doesn’t have sampling error!” Respond calmly and accurately, as if you were a teacher speaking directly to the two students in an attempt to de-escalate the argument and educate them in correct terminology.
3.	Does the size of the sample affect the variance of a sampling distribution? ___ Does the size of the population affect the variance of a sampling distribution? ___ Elaborate on each answer with approximately one sentence.

4.	Identify each scale below as nominal (N), ordinal (O), interval (I) [same as “arithmetic”], or ratio (R).
(a)	French fries are available in serving sizes S, M, L, and XL (extra large).
(b)	Awards for top salespeople are at the Diamond, Platinum, Bronze, Gold, Uranium, Velvet, Ruby, Emerald, Topaz, Rhodochrosite, or Silver levels.
(c)	The temperature outside is 45° F. Tomorrow, it will be colder by a few degrees, but on Thursday, it will be warmer by a few degrees.
(d)	Cereal boxes are available in 12, 18, and 24 ounce sizes.
5.	Does it make any sense to say that a sunny 70-degree day is twice as warm as a chilly 35-degree day? Why or why not? (Explain briefly.)

6.	The Drench people are heavyset, with a weight that follows N(177, 22) in pounds. The Glermans, by contrast, are somewhat svelte, with a weight that follows N(154, 25) in pounds. If a Drench person and a Glerman person are randomly paired, compute the probability that the Glerman is heavier. Show relevant work, and clearly identify any random variables that you use.
7.	In #6, explain why the answer cannot be computed if Glermans and Drench are allowed to choose their own partners freely.
8.	Random variable X has mean 4 and variance 3. Random variable Y has mean 5 and variance 2.5. The variables are given to be independent. Compute E(X – 2Y) and sX – 2Y, showing correct notation and a bit of work.

	For the remaining problems, categorize the situation as binomial (B), geometric (G), or neither (N). Then compute the requested probabilities, showing your work.
9.	You draw cards from a well-shuffled deck, replacing and reshuffling between each draw. We are interested in how many of a certain type of card you can draw.
(a)	Situation: ____
(b)	Compute the probability that 3 or more face cards are selected in 7 draws. A “face card” is defined to be a jack, a queen, or a king, and there are 12 of them in a standard 52-card deck.
(c)	Compute the probability that no more than 2 of the 7 cards have a value of 9. (There are four nines in the deck.)
10.	This is the same situation as #9, except that the deck is not reshuffled or restored between draws.
(a)	Situation: ____
(b)	Compute the probability that at least one of the first 7 draws is an ace. (There are 4 aces in the deck.)
11.	This is the same situation as #9, except that we are interested in how many draws are needed to obtain an ace.
(a)	Situation: ____
(b)	Compute the probability that more than 4 tries are needed to obtain an ace.
(c)	Compute the expected number of tries to obtain an ace.