spring 2009 - Spring, 2009 Economics 210 ECONOMIC...

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Unformatted text preview: Spring, 2009 Economics 210 ECONOMIC STATISTICS Exam #2 HONOR CODE (“1 have neither given nor received unauthorized aid on this exam”): Signature You have up to two and a half hours to complete this 100 point exam. Be brief and to the point since only the main point(s) asked for in each question will aid your grade while a display of ignorance can count against you. One point (up to a maximum of three points) will be deducted (from any extra credit points you may have accumulated) for each misspelled word in either the “Honor Code” (which I ask you to write out) or in your answer to a question in which the same word is used (and spelled correctly). Pleasedo all the questions and showyour work. (No credit without an explanation. Correct answers without any work will be penalized.) Do you remember the climactic scene in the movie “Raiders of the Lost Ark” when the Nazis open up the Ark of the ' Covenant, out surges a terrifying horde of evil fury and the Nazis’ heads melt like “chocolate bunnies in a microwave”? Well, then, you’re ready to open up this exam. Good luck. . ONE wAVlsTOANALYZEJvéT .v , ‘ . _ > THAT’s I. WWLOfiT.JK‘(—1DFIGUKE -. ~ .' THEOTHEQ - * owwHATWWwERE, -, V. .1 ‘ _ -: ANOTHENTR‘HO lMPflOVEéO - 1‘ ' THAT NEXT TIME '{ou CAN wIN .. l. (15 points) People with O-negative blood are called “universal donors” because O—negative blood can be given to patients with any blood type. Only about 6 percent of people have O-negative blood. The Red Cross gets its supply from volunteer donors who show up more-or—less at random. We can use the binomial formula to model the arrival of donors with various blood types (which in turn helps Red Cross managers plan their blood allocations). Suppose that 25 Students arrive at a Red Cross Blood Drive'in McCullough to give blood. (2) a. How many (of the 25 students) can be expected to be universal donors? (3)" b. For this group of 25, what is the standard deviation of the number of universal blood donors? (4) c. What is the probability that not one of the 25 students is a universal donor? (6) d. hat is the robabili that there are exactly 3 or universal donors out of the W p ty 4 25 students? 4' i'z [ET ‘ .m... 3 ,. I)? . ATI’ (1517 3’ flaws “'3 /. /X + ax as x (fizaésmge “2/3 v J’ i {MB 5" 59%? Wisma :2 (fl /"7 i 272% a? “new; we’d? fiver? ' , . / 6&1?de 5 err cMMe/Ezcz/ joWfl/fi 4mm . / ' l 2. ’ <2) (3) . (4) (6) (15. points) Pixel Perfect, a company that manufactures large LCD screens, knows that not all pixels on their screen light up, even if they spend great care making them. In a sheet 6 feet by 10 feet (or 60 square feet) that will be cut into smaller screens, they find an average of 4.7 blank pixels. They believe that the occurrences of blank pixels are . independent (and that the number of blank pixels can be modeled by a Poisson random variable). Their warranty policy states that they will replace any screen sold that shows more than 2 (two) blank pixels. a. To four decimal places, what is the mean number of blank pixels per square foot? b. To four decimal places, what is the standard deviation of blank pixels per square foot? c. What is the probability that a 2 foot by 3 foot screen will have at least one defect (that is, at least one blank pixel)? d. What is the probability that a 2 foot by 3 foot screen will be replaced because it ' has too many defects (that is, more than two blank pixels)? 3. (15 points) Suppose that the distribution of oil prices ($/bbl or dollars per barrel) is forecast next winter to be a triangular distribution with a loWer limit of $40/bbl, an upper limit of $100/bbl, and a mode of $60/bb1. There are two branches to the probability 1 density function (pdf) for x: K 40: 560 =——— —40 x prx) 600(x ) 60<x_<_100 p(x)=— ’1 (x—IOO) 1200 (2) a. Find the probability that oil prices next winter will be less than $60/bbl. (3) b. Find the probability that oil prices next winter will be greater than $80/bbl. (6) c. Find the median oil price. (4) l d. Find the mean oil price. {Hintz For 1 point partial credit, will the mean be less than or greater than the median in this problem?} 5M /3 fit/$634453???” ' = ‘ A? _.L if” .L ( §a5[ b, '3 2600'0gagz—fzw. Z) / c & .1 (haw/V75; ' 4406 "My; "3? i200 , ~ 1/ ' MW r" g 3.47% 4‘ “z? «a wfiflflj i) Wife“ v- 61; z Ami/e # 5' 3‘ éééV/La (4) (4) (4) 4. §I>Zfi<<iizwb z/‘gfz4 (12 points) The business of a British company called “Molegon” was to remove unwanted moles from gardens. The company kept records indicating that the population of weights of moles in its region was approximately normal, with a mean of 150 grams and a standard deviation of 56 grams. a. What proportion of all moles weigh less than 200 grams (or about 7.05 ounces)? b. Eighty (80) percent of all moles weigh more than how many grams? 0. Suppose that the European Union announced that only moles weighing between 68 and 211 grams (inclusive of these end values) can henceforth be legally caught. “Molegon” wants to know what percent of all moles can be legally caught. What then is that percentage? _ _ 21 g! l s {mm/5’6 _ 5b Z 'i {Sgépg 1L ;. E3 ig/gg g/.‘33%2M%+5 [x5 XA 1&9 ' ’ .ga‘j 42> 220 (a my - r 5. (15 points) Suppose the Dew Drop Inn has 85 rooms. At this .time of the year, the average daily room occupancy rate is, say, only 45 percent. The average charge per room (per . night) is, say, $100. Let x denote the number of rooms Occupied on a given night. (3) a. Find the mean and standard deviation of the number of rooms occupied per night (during this time of year). (2) b. Find the mean and standard deviation of income that will be earned by the Dew Drop Inn per night. (4) c. What is the binomial probability that 35 or fewer rooms are occupied on a given night. Set up this part of the problem. Do not solve. Please use a summation k sign, 2 . Please specify values for “j” and “k”. And, place the binomial formula x=j ' inside the summation Sign, with appropriate values for “n” and “1t”. (6) (1. Use the normal approximation to estimate the probability in part (c). a . I_ - _ .7 , . // l 474%? AL KSZS/ Mam/i .’ 3‘— ’ 1'2 QKZCS . ’x/nj/l/Kfarttéf: ‘2‘ $453,, ‘ 2 g: toga—wear" . " "’26 H \ .. . g4 (1’ if" 55%53‘1553 K X333 6. (6 points) Concern over the weather associated with El Nifio has increased interest in the possibility that the climate on Earth is getting warmer. The most common theory relates an increase in atmospheric levels of carbon dioxide (C02), a greenhouse gas, to increases in temperature. A regression predicting mean annual air temperature (over both land and sea across the globe) in degrees Celsius (C) [the response variable] from the mean annual C02 concentration in the atmosphere, measured in, parts per million (ppm) at the top of Mauna Loa in Hawaii [the predictor] produced the following results: Predictor Coefficient Constant 15.3 066 CC; 0.004 R—squared = 33.4% (2) a. What is the correlation between C02 and mean temperature? (Note: Please report the correlation coefficient to two decimal places} (2) b. C02 levels may reach 364 ppm in the near future. What mean temperature does the regression model predict for that value? {Note: Please report your answer to two decimal places} (2) c. By how much would C02 levels have to increase to raise the mean temperature by exactly one degree Celsius (C)? {Note: Please report your answer to the nearest whole number of ppm} 1 W39 it /5’ 5345‘ ‘7'“. I “2 /é:%‘:{£jiees ‘ ‘ '2 [meat Z932, (1) (2) (6) (3) (3) (15 points) Data were collected for gross leasable area (x, the predictor) and retail sales (y, the dependent variable) in shopping malls in n = 24 randomly chosen states (one shopping mall per state). The leasable area is expressed in millions of square feet and retail sales are expressed in billions of dollars. The following computations were obtained: in =‘3765 2y. 2984.5 2x} = 1352341 2y} ; 92665.8 _ 2w, =3517504 Assume that there is a linear relationship between Area (x) and Sales (y) as follows: Sales = b0 blArea . 3. Would you anticipateaositigro, or negative slope coefficient? b. For every one unit incr'egs in'Area (here, 1 million square feet), will Sales increase by: (i) b0 or (iii) b0 +bl ? c. Find the ordinary least squares estimates, b6 and b1 . d. If leasable area in a shopping mall is 100 million square feet, what would you predict retail sales to be (in billions of dollars)? e. If leasable area in a shopping mall is equal to ; , would predicted sales be greater tha@, or less than y ? V ““““ ""2 - e,- -. .,_ .,_ ,. 5754 $215 3 g ‘ z 39’ 79d“) «4" » 24 , 24 g ,- “" /- 'i 52‘ $925+! 2% (7 points) The National Bank of Middlebury (NBM) is presented with car loan applications from 10 people. The profiles of the applicants are similar, except that 5 are minorities and ‘5 are not minorities. In the end, NBM approves 6 of the loan applications. If these 6 approvals are chosen at random. from the 10 applications, what is the probability that less than half the approvals will be of applications involving minorities? {Hint In this problem, you are samplingwithout replacement, that is, the probability of choosing a minority loan applicant changes with each selection. For 1 point partial credit, what is the name of the appropriate probability distribution to use to answer this question?} [jib Giza, ivy/Mm cfiémla'fiéa , V/u / z W “a, , _ : Zeta/$1] 9%,? fl/tfiaQ-ztflé Wilma}; 59$ mafilfée. Lg We? M/[M/y I L AREAS UNDER THE STANDARD NORMAL CURVE This table shows the area between zero (the mean of a standard normal variable) and 1. For example, if z = 1.50, this is the shaded area shown below which equals .4332. z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359 0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753 ' 0.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141 0.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517 0.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879 0.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 ' .2157 .2190 .2224 0.6 .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2517 » .2549 0.7 .2580 .261 1 .2642 .2673 .2704 .2734 .2764 .2794 .2823 .2852 0.8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133 0.9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 .3389 1.0 ‘ .3413 .3438 .3461 .3485 .3508 .353 1 .3554 .3577 .3599 .3621 1.1 .3643 .3665 .3686, .3708 .3729 .3749 .3770 .3790 .3810 .3830 1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015 1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177 1.4' .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319 1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441 1.6 .4452 .4463 .4474 1.4484 . .4495 .4505 .4515 .4525 .4535 .4545 1.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633 1.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706 ' 1.9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767 2.0 .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .4817 2.1 .4821 . .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857 2.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .4890 2.3 .4893 .4896 .4898 .4901 .4904 .4906 .4909 .4911 .4913 .4916 2.4 .4918 .4920 .4922 .4925 .4927 .4929 .4931. .4932, ~ .4934 .4936 2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .4952 2.6 .4953 .4955 . .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964 2.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974 . 2.8 .4974 .4975 .4976 .4977 .4977 .4978 .4971 .4979 .4980 .4981 2.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .4986 3.0 .4987 .4987 .4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990 Source: This table is adapted from National Bureau of Stahdards. Table: of Normal Probability Func- lions. App1ied Mathematics Series 23, 0.5. Departmental Commerce. 1953. ...
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spring 2009 - Spring, 2009 Economics 210 ECONOMIC...

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