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FINAL PROBABILITY AND STATISTICS, ECON 15A
DECEMBER 7, 2011 Use for questions 1 — 3. The right side of a person’s face is said to resemble the whole face more than the left side does. Kennedy, Beard,
and Carr (1982) asked 91 subjects to View fullface pictures of six different faces. Testing for recall was conducted one week later, when
subject were presented with pictures of twelve faces and were asked to identify the ones they had seen earlier. At testing, subjects were
divided into three groups of roughly equal size. One group was presented with fullface photographs, one group saw only the right side of the face, and one group only saw the left side. The researchers then recorded the number of errors each subject made. The highest level
of education for each subject was also recorded. 1 — 2 (two questions — twenty points.) What are the variables and what are the categories of the variables? Please list each variable and
then, next to each variable name, list the categories in parentheses. Then state the scale of measurement (nominal, ordinal, interval, ratio) for each variable. If there are more than six categories, you only need to list six of them. Finally, you need to indicate the dependent
variable with an asterisk. (You will lose ﬁve points for each error.) VARIABLE (CATEGORIES) SCALE OF MEASUREMENT
Wrawﬁaca (FL/Lu, ZiaHT, LET—‘7‘) NOMINALN
ale NUMBEZ. 0F 222025 [0,1, 2, 3, Li, 5,4) ZAT‘LO
LEVEL 0? ED. (WWI; HS, AA, BA, HAN/i117) ozvmaun 3. If I calculated mean number wrong for the 91 subjects, it would be called a) a sampl®a statistic, c) a population, (1) a parameter. 4. Estimate the ﬁrst quartile for the below distribution. 15 mi, @3911” 13—4/7 0 10 20 30 5. Here’s some data for how long it takes to get to school. Draw a histogram for it using a densigz vertical scale. Be sure and put
values on the horizontal axis. (For this graph, please put values on the XAxis for the boundaries (real limits) of the categories.) Time Relative Frequency 08 8 1 812 12 3 3
1214 8 2
1418 16 I: 1826 24 3 I
2630 12 3 3046 16 , 4650 4 I 6. The second central moment of a distribution equals the second moment from the origin minus what? (Your answer needs to include atypeofmoment.) T146 F1261, MOHM WM "THE 0Z1 41L) 7. True or false (and explain): Lambda only measures the linear relationship between two variables.
PALSE A LAW WTLOQSHIP WITH:
Mar/(muse. 2293328311“ Eda) WEBE 8. In a rectangular distribution, what percentage of the scores lie within two standard deviations from the mean? (Be sure to pause, and
think about the shape and what its standard deviation is.) lOOZ> +2. 9. V(X — Y) = V(X + Y). What do we know about variables X and Y? Please explain how you know this. V(X—Y): VCK) 1' «(‘0 " ZCUVCXH’) Thus wVCxVD __= O V5x+Y)' V(X) er‘f) 4' Zea/(KY) THUS @ 10. Let X be a random variable such that p(X=1) = .4, p(X=4) = .4, p(X = 10) = .2. Let Y = X2. What is E(Y)? Li ti, HVG'LHZOSLZE
O Q
10 100 .Z Z. Use the following for questions 11 — 14. There is a parking lot with twelve cars for sale. There are two yellow Mustangs, one red
Mustang, and three blue Mustangs. There are two yellow Ferraris, three red F erraris, and one blue Ferrari. Assume that each car has an
equal probability of being sold. (Cars are not returned, so all the questions are without replacement.) 11. What is the probability that the ﬁrst car sold is 21 Mustang and the second car sold is a Ferrari? 12. What is the probability that either the ﬁrst car or the second car sold is a Blue Ferrari? 0“ lsr ml; THIN/ALL“? Pause) a F00 rFCB>=S/IZ + X1 13. What is the probability that either the ﬁrst or the second car sold is a Mustang? ‘5; 23:: More = me We lee/15> r Vlad/12 “(é/2" 7“ 14. What is the probability that the car is a Ferrari, given that it is red? 0 (#125161 mail 15. A certain typist, on average, makes three errors per tenpage document. What is the probability that this typist/ﬁill make three or
more errors in this tengage document? Assume that a Poisson distribution is appropriate. .. ' z —3 1 ~25 0 —
1 Z ea [£55 3 c 5
I, C Q; + 8 9T 4. 7 !~ ZZ‘TOL1+.I‘9756+.OLI?79 Z t I I O I I i '— 16. In a test for ESP, a subject tries to identify what is on the back of a card. The experimenter can see the back, but the subject cannot.
The cards contain either a star, a circle, a wave, a square, or an X. Each of these options is equally likely and the selection is random, A subject looks at 25 cards, and correctly identiﬁes seven of them. What is the probability of getting seven or more correct simply due to
chance? (Please feel ﬂee to use a normal approximation without a correction for continuity.) 17% EV=’/5x25:5 = ZS 5 , r”
N 3],. i/SXzSXQ/S‘rz‘ 5 7
17. The probability of being bit by a rattlesnake is .0001. Amy wants to know the probability 10 or fewer people being bitten in a population of 100,000 people. (Of course we are assuming equal and constant probabilities as well as independence of events.) Amy
wants to be as accurate as possible (even to ten places after the decimal point). Should she use the binomial distribution, the normal distribution, or the Poisson distribution? No need to explain.
5 1w H 1 AL... 18. TEN FREE POINTS! (But if you want to waste time — you get ten points whether you answer this or not — tell me what is the best
the following seven: apple, pumpkin, blueberry, coconut creme, mince, or Shooﬂy? Explain why.) 51,. ,‘ﬂj Mopbﬁjai é‘fooSPLESS, ...
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This note was uploaded on 12/13/2011 for the course ECON 15A taught by Professor Shirey during the Fall '08 term at UC Irvine.
 Fall '08
 Shirey

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