STAtistics / Mr. Hansen 12/9/2008

Name: _________________________ Battery bonus (Mr. Hansen’s use only): __________

Cumulative Test through Chapter 8 (100 points)

• Illegible or cryptic explanations may not earn full credit, even if your answers are numerically correct. In particular, the letter z must always be crossed.
• Decimal approximations should always include at least 3 significant digits.
• Do not mark on your formula sheets. These are to be reused all year.
• If you happen to have spare batteries, leave them in plain view for a 1-point bonus.

Part I: Always, Sometimes, Never (2 pts. each)

In the small blank, write A if the statement is always true, S if sometimes true, or N if never true.

___1.	If A and B are events, then .
___2.	If A and B are events, then .
___3.	Residuals for a LSRL have a sum of 0.
___4.	If , there is more than one line that minimizes .
___5.	“House effect” refers to sampling error, i.e., random variations between samples.
___6.	An r value close to –1 implies strong linear correlation.
___7.	A statistically significant result occurs by chance.
___8.	A P-value of less than 0.05 constitutes statistical significance.
___9.	The P-value tells us the probability that chance alone caused a certain result to appear.
__10.	The P-value is a conditional probability, namely the probability of finding results as extreme as or more extreme than the ones observed, given that chance alone is the only force at work and there is no actual difference between the experimental and control groups for the parameter being sampled.

Part II: Definitions (4 pts. each).
Give a concise, reasonably accurate definition of each term.

11.	statistical significance
12.	ordinal scale
13.	normal quantile plot
14.	independent
15.	random variable

Part III: Probability (60 pts., 6 pts. per numbered question): JUSTIFY ANSWERS!

Proper notation is required for full credit. Answers alone are worth 2 points per question. The remainder of the points are for proper notation and justification. In general, you must furnish setup (often a formula), plug-ins, and answer.

	For questions 16-21, assume that Carl sinks approximately 82% of his free throws and that the shots are independent.
16.	Define a suitable random variable for the number of tries needed for Carl to sink his first free throw. Identify the setting by name, and explain how you know that all the conditions are met.
17.	Compute the probability that Carl sinks his first free throw in fewer than 4 tries.
18.	Define a suitable random variable for the number of successful free throws Carl obtains in 18 trials. Identify the setting by name, and explain how you know that all the conditions are met.
19.	Compute the probability of more than 12 but fewer than 15 successes in 18 tries.
20.	Compute the expected number and variance for the number of successes in 18 tries.
21.	Compute the expected number of shots needed in order for Carl to obtain his first success.
22.	The incidence of TB in a large city is 1.2%. An SRS of 700 residents is selected. Explain why the binomial distribution for the number of TB-afflicted people in the sample is not correct but is nevertheless close enough for estimation purposes.
23.	Under the same givens as in #22, compute the probability that an SRS of 65 residents contains at least one TB-afflicted person.
24.	The probability of “two pair” on the deal in 5-card draw poker is 123552/2598960, as we computed in class some weeks ago. Prove this result. (“Two pair” is defined as two cards of one value, two cards of another value, and one “junk card” drawn from the remaining 44. There are 52 cards in a standard deck, consisting of 13 values and 4 distinguishable cards of each value.)
25.	A woman plays 600 hands of 5-card draw poker. Compute the probability that the number of times she receives “two pair” on the deal is 21, 22, 23, 24, 25, 26, 27, 28, 29, or 30. If possible, please use a time-efficient method.