Test on Regression and Probability (CFU)

STAtistics / Mr. Hansen	Name: _______________________________________
11/24/2009

		Year	$/MB
		1979	1000
		1988	20
		1993	2
		2009	.0001

1.	Fit a line to the time series scatterplot of “number of megabytes per dollar.” [Note: This is different from the column shown. Good thing this was only a practice test!] Show points, LSRL, and equation.
















2.	Plot residuals for #1.
















3.	Find (a) an exponential regression and (b) a power regression equation for your scatterplot in #1.


4.	Which fit is best for #1: linear, exponential, or power? Justify your answer.

5.	We will draw 2 cards, with replacement, from a well-shuffled deck. In other words, the deck will be shuffled thoroughly between the draws, and each card will be drawn from a pool of 52. Let A be the event that a 7 is drawn on the first draw, and let B be the event that either an 8 or a 9 is drawn on the second draw. Are A and B mutually exclusive? (Write “yes” or “no.”) _______ Are A and B independent? _______ Compute , correct to 6 decimal places: _______

6.	In the universe of students, the probability of diligence (event D) is 0.4, and one fourth of students earn an A (event A). Among the students, 55% are diligent or earn an A (or both). Draw a Venn diagram to illustrate the universe, as well as the relationship among events A and D. Use the blank region below. Also state the following to 3 decimal places of accuracy: = _______ P(A \| D) = _______ P(D \| ~A) = _______ P(D) = _______ = _______ Explain carefully why A and D are independent but not mutually exclusive. Label the probabilities that you use in your proof.

7.	Two fair dice are rolled.

(a)	Compute the unconditional probability of an even sum. Work is required for credit.















(b)	Now suppose that I can see the outcome of the roll of the dice, but you cannot. You ask me, “Mr. Hansen, is at least one of the two dice showing an even number?” I respond, “Yes.” Does this increase or decrease the likelihood that the sum of the two dice is even, or does the probability remain the same? Show your work (no credit without work).















8.	I feel lucky, and I think I can roll an 8 on my next roll of the dice. You think this is unlikely, and you offer me odds of 6:1. Is this a fair game? _______ Compute the expected value of the game to me for each dollar that I wager. (Work is needed for credit.)

9.	Write a simulation methodology to address the following question. Do not actually solve the problem. There are 20 people at a party. Each person will be given a ticket with a random integer from 00 to 19 printed on the ticket, and each number is used exactly once. How likely is it that the ticket number you receive is greater than the mean of the ticket numbers of the 5 people closest to you?































10.	Compute the probability that an SRS of 5 people attending the party in question #9 would include at least one person with a ticket number in the top 5. (The top 5 numbers are 15, 16, 17, 18, 19.) Give answer to 3 decimal places. Work is required for full credit.

11.	Consider the 5 trials in question #10.

(a)	State why these trials are not independent.



(b)	Does it make sense in a situation like this to use the letters p and q? Why or why not? [Remember, p = single-trial probability of success, and q = 1 − p. These are standard definitions in statistics classes everywhere.]






12.	A screening test for superslobberiness is 98% sensitive (i.e., P(pos. \| infected) = 0.98) and 97.5% selective (i.e., P(neg. \| not infected) = 0.975). Compute the PPV of the test if superslobberiness affects 1.5% of all dogs. PPV stands for “positive predictive value” and is defined as P(infected \| pos.).