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AP Statistics / Mr. Hansen |
Name: _________________________ |
CFU in Preparation for Test on 1/31/2001
The test will cover §7.2 (mean and s.d. of combined r.v.’s), §8.1 (binomial distributions), §8.2 (geometric distributions), as well as experimental design (blinding, blocking, control, randomization, replication, matched pairs, etc.).
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1. |
In order to demonstrate a cause-and-effect relationship, we must perform ________________ , which means that we administer a _____________ while controlling as many of the ______________ variables as we can reasonably afford to. The 3 key principles in designing a study of this type are __________ (by which we mean ______________________________________ ), __________ (by which we mean ______________________________________ ), and __________ (by which we mean ______________________________________ ). |
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2. |
The technical purpose of blocking in experimental design is to ______________________ _________________________________ . This is a good thing to do (i.e., there is a real-world purpose or goal to performing blocking) because ___________________________ ________________________________________________ . |
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3. |
Any study in which the subjects know when they are being treated and when they are not being treated may be susceptible to the ___________________ effect. |
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4. |
Systematic discrepancies in the probability that certain members of the population are selected for a study, or selected for treatment, or selected for response, or treated in any way differently from other members of the population are all examples of _________________ . |
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5. |
Subjects in a certain imaginary experiment are randomly chosen to receive an all-expense-paid trip to Seattle for a mathematics conference. Their scores on a standardized achievement test measuring mathematical knowledge are computed before and after the trip. This design uses ________________________________ . |
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6. |
Subjects in another imaginary experiment are randomly chosen to receive a low dose of aspirin daily or a high dose of aspirin daily. This design exhibits _________________ . |
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7. |
Subjects in a third (and final, I promise) imaginary experiment paint the left side of their noses with one skin cream, the right side with another, and the bridge of their nose with a third. This design exhibits _________________________ . |
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8. |
If heights of cornstalks in Farmer Bill’s field (in feet) are distributed according to N(6, 0.8) and if Farmer Irene’s are distributed according to N(6.5, 0.95), what is the probability that a randomly selected cornstalk from Bill’s field is taller than a randomly selected cornstalk from Irene’s field? For full credit, state any assumptions you are making. |
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9. |
What happens to the mean of a r.v. if all values are increased by 4? ____________ What if all values are quadrupled? _________________ |
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10. |
What happens to the s.d. of a r.v. if all values are increased by 4? ____________ What if all values are quadrupled? _________________ |
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11. |
If temperatures on the Frizzlewatt scale in West Siberia are normally distributed with a mean of 15 and a s.d. of 14, what are the mean and standard deviation on the Fahrenheit scale? Assume that Frizzlewatt degrees = 4 · (Fahrenheit degrees) – 10. |
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12. |
Classify the distributions of each of the following random variables as normal, approximately normal, binomial, approximately binomial, geometric, approximately geometric, or none of the above. If you choose any answer other than "none of the above," state the parameters of the distribution and answer the remaining questions. |
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(a) |
X = # of spades received in a bridge hand (13 cards) |
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(b) |
X = # of free throws made in 40 attempts, where the probability of success per trial is initially 0.6 but improves slightly with practice |
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(c) |
X = # of double sixes received when Belinda rolls a pair of fair dice 120 times |
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(d) |
X = # of phone calls made by Leisure Suit Larry to get a prom date, where the probability of success per call is approximately 0.2 |
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(e) |
X = length (in cm) of the right big toe of American men, where the median is 5 and 68% of these men have toes measuring between 4.2 cm and 5.8 cm |
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(f) |
X = # of die rolls needed to get either a 3 or a 6 |
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For your own benefit, fill in the purpose and syntax of each of the following TI-83 functions. You are permitted to store "cheat hints" in the memory of your calculator if you wish. (Last year, Doug Bemis wrote a program to prompt for the needed values.) |