S21MidtermStudyGuide - Hank Ibser Statistics 21 Spring 2010...

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Unformatted text preview: Hank Ibser Statistics 21 Spring 2010 Study Guide for the Midterm The midterm (Tuesday March 9 in lecture) will cover the following chapters with certain parts omitted: Ch1—2: Concepts and terminology in these chapters will be included as relevant to Ch 12. Read section 1 of each chapter. Ch3: Omit sections 5—7. Ch4: Omit stuff on longitudinal/cross—sectional data in section 2. Omit section 7 unless you are using a calculator to find SDs. Ch5: Omit interquartile range (p89). Ch6,7: Omit. If you are looking for extra problems to do, the Special Review Exercises at the end of Ch 6 are good because they incorporate ideas from different chapters. Try l,2,3,4,6,7,9,ll. Ch 8: Omit Review Ex #12. Ch 9: Omit technical note on p146—l47 although I think it's interesting to compare this to the rms error for regression. Ch 10: Omit technical note on p169. Ch 11: Omit section 3 and technical note on p197. Ch 12: Omit, in section 2, everything from "Now, an example." to the end of the section (p208—211). Omit section 3. Omit Review Ex #12. Ch 13—15: You are responsible for everything in these chapters. More extra problems: Special Review Ex after Ch 15: 8—9, 11—15, 17—20. Handouts: "Summation, Average, and SD," "Summation and Correlation," and "Probability." The following 11 problems are from my old midterms; they tend to focus on the handouts since you don't have practice from the text. After those are 27 problems from old midterms of Roger Purves (one of the authors of your book). His problems tend to be shorter and there are more probability problems (all on the last page). The midterm will have 5—6 problems. I also encourage you to do extra problems from the book as well as making up problems and exchanging them with people. Look on bspace for updates on review times and SLC services. 1) I have two bags of fruit. The first contains 4 apples and 2 oranges, the second contains 5 oranges and 3 bananas. I choose a bag at random and then take 4 pieces of fruit from that bag to eat for lunch. a) What is the chance that the 4 pieces of fruit are the same? b) What is the chance that I get at least one orange? 2) I record daily high temperatures in Berkeley for 90 days. The average of the first 30 days is 70 degrees Fahrenheit with an SD of 8 degrees. In the next 60 days, the average is 60 degrees with an SD of 6 degrees. a) What is the average temperature for all 90 days? b) What is the SD of temperature for all 90 days? 3) A list of transactions contains 100 numbers: 60 gains and 40 losses. The gains are positive numbers and the losses are negative numbers. The units are thousands of dollars. For the 60 gains, the average is 18 and the SD is 7.5. For the 40 losses the average is —20 and the SD is 9.2. a) Find the average of the 100 transactions. b) Find the SD of the 100 transactions. (If you didn't get an answer for part a), use overall average=4.) 4) The following information was collected for a group of women: Average height = 65 inches SD of height = 2 inches Average weight 130 pounds SD of weight = 20 pounds r= 0.4 (a) Predict the weight of a woman who is 68 inches tall. (b) Of the women 68 inches tall, what percent weigh more than 130 pounds? 5) I roll a fair six—sided die 4 times. a) What is the chance that I get exactly 2 fours? b) What is the chance that not all the rolls are 2 or more? c) What is the chance that I get exactly 2 ones or exactly 2 sixes? 6) Incomes in a certain town follow the distribution below. 1000's of $/year % of Town 10—20 10 20—30 25 30—50 30 50—70 20 70—100 15 a) Draw a histogram for this data, labeling axes and including density scale. b) About what percent of the people in this town earned between 50 and 55 thousand dollars? c) About what are the average, median, and SD for these incomes? Choices are: 10,000, 20,000, 35,000, 40,000, 45,000, and 50,000. You obviously won't use all the numbers and shouldn't use any numbers more than once. Average: Median: SD: 7) At one university, the average Verbal SAT (VSAT) score of the incoming freshmen is 550, and the average Math SAT (MSAT) score is 530. The correlation between VSAT and MSAT score is 0.6. The equation for predicting MSAT score from VSAT score is reported as: predicted MSAT score = 0.9 (VSAT score) + 10 Does this line make sense? Pick one of the following and explain. (i) It doesn‘t make sense, that isn‘t the regression line. (ii) It does make sense, that's the regression line. (iii) We do not have enough information to tell if it is correct or not. 8) At a university, a group of 200 freshmen has an average VSAT score of 550, and the average MSAT score is 540. The correlation between VSAT and MSAT score is 0.6. The SDs for both exams are 100. A group of 100 sophomores has an average VSAT score of 550, and an average MSAT score of 600. The SDs for both exams are also 100. The correlation between VSAT and MSAT scores for the sophomores is 0.5. (This is a too long for a midterm, but good practice.) a) Find the average VSAT and MSAT scores for all 300 students. b) Find the SDs for VSAT and MSAT scores for all 300 students. c) Find the correlation between VSAT and MSAT scores for all 300 students. 9) The distribution of heights of a group of women closely follows the normal curve. A woman at the 84th percentile of heights is 67 inches tall, and a woman at the 7th percentile of heights is 61 inches tall. (a) The average height is inches. (b) Someone at the 20th percentile is inches tall. 10) A drawer contains 20 socks. Ten of the socks are white, five are brown, four are gray, and one is red. a) You take two socks from this drawer at random without replacement. What is the chance that they are both the same color? b) 3 socks are drawn without replacement. What is the chance that exactly 2 white socks are drawn? 11) The midterm scores for a large math class were recorded as follows: Midterm 1: average e 110, SD = 15 Midterm 2: average = 95, SD = 13, r = 0.5 (a) Find the equation of the regression line for predicting midterm 2 _score from midterm 1 score. (b) Predict the mt 2 score of someone at the 47th percentile on mt l. Answers to my problems: 1) a) (1/2)(4/6)(3/5)(2/4)(1/3)+(l/2)(5/8)(4/7)(3/6)(2/5) b) 1—((l/2)(4/6)(3/5)(2/4)(1/3)) 2)avg=63.33, SD=8.47 3) avg=2.8, SD=20.35 4) a) 142 pOunds b) 74% 5) a) 41/21/2! (1/6)A2 (5/6)“2 b) 1—(5/6)“4 c) 2*(answer to a) — 41/2l/21 (1/6)A2 (1/6)“2 6) a) don't forget density scale... b) about 5% c) avg=45,000, median= 40,000, SD=20,000 7) (i) point of averages isn't on the line. 8) a) 550,560 b) 100, 103.923 c) 0.54528 (rounding is OK) 9) a) avg=64.6 b) 62.6 10) a) (10/20)(9/19)+(5/20)(4/19)+(4/20)(3/19) b) 3(10/20)(9/19)(10/18) 11) a) predicted mt2 = 0.433 mtl + 47.33 b) about 94.5, answer may vary a bit, I used —0.075 for 2. Answers to problems from Roger Purves' Stat 21 past midterms: 1. a) 1 b) 2.83 2. 1 3. a) False b) must be negative 4. 6% 5. 50 pts 6. a) 62 b) 67% 7. a) 0 b) 4 8. about 96 students 9. a) 1 b) % of families per thousand dollars c) 5% d) less than $40,000 10. a) 0.58 b) —1 11. a) 200 b) 135 12. a) 52,000 b) 12,247.5 13. 52.2 14. a) 27.5 b) 3.23 15. a) Blst percentile b) 60% 16. smaller than 190 17. about 255 students 18. 4.58 19. 1/45, 1/90 20. 26/52 x 25/51 x 26/52 x 25/51 21. a) (1/6 x 1/6) + (5/6 x 4/6) b) 1—[(1/6 x 1/6) + (5/6) X (4/6)] 22. 20/100 = 1/5 23. 16/25 24. a) 51.8% b) 19.75% c) 1.08% 25. 39/52 x 38/51 26. 13/52 x 39/51 x 38/50 x 37/49 x 12/48 27. 8/20 Statistics 21 Problems from past midterms _ {gage-r Perv-£5) Midterm 1 1. (10 points) A list of numbers has an average of 51. A new list is formed by subtracting 50 from every number on the original list. The r.m.s. of the numbers on the new list is 3.0. ' (a) Find theaverag‘e on the new list. (1)) Find the so of the original list. 2. (10 points) One number is missing in the data set below: moor—n— >4 LDNM “d If possible, fill in the blank to make the correlation coefficient equal to 0. If it is not possible, ‘ say why not. 3. (10 points) An instructor gives tWo quizzes to the ten peeple in her course. On the first quiz, five of the people were above average; but on the second quiz, these people all scored below average. The other five people moved in the opposite direction. They were all below average on the first quiz, and above average on the second one. (a) True or False and explain: “This is an example of the regression effect.” (b) The correlation coefficient between the score on the two quizzes: must be zero. ' must be a positive number. must be a negative number. _ could be any of the above, depending on whether or not there are outliers in the data. Check (NI) one option. Explain your choice. 4. (10 points) Here are the summary statistics for a large group of male students at a certain uniVersity. Height: average =' 70 inches, SD = 3 inches Weight: average == 162 pounds, SD = 30 pounds correlation coefficient = 0.50 The scatter diagram is football shaped. About what percent of the men 74 inches tall weigh less than the average weight of the men 66 inches tall? . 5. (10 points) In the mid—1980’s, the Educational Testing Service compared the SAT scores of college-bound seniors with those obtained by a large representative sample of high school juniors. On the verbal SAT, the 40th percentile of the scores for the college-bound seniors happened to be equal to the 60th percentile of the scores for the sample of juniors. For both groups, the SD was 100 points. The two histograms followsd the normal curveclosely. Find, approximately, the number of points separating the average of the two groups. f x . 6. (10 points) Here are the summary statistics for a very-large class: midterm score: average = 57 points, SD = 13 points final score: average = 52 points, SD = 25 points correlation = 0.80 The scatter diagram is football shaped. (a) One person in the class scored 66 points on the midterm and 59 points on the final. What would be the regression estimate of his final score from his midterm score? (b) Out of all those who got the same score on the final as he did, what percent scored below him on the midterm? a; -( 5 gainer) A. list of numbers has an r,m.s. of 4.0. A new list is formed by adding 3 to every . number on the list. The new-list has an r.m.s. of 5.0. ‘ (a) Find the average of the original list. (b) Find the SD ofthe original list. ,8. (5 points) An instructor in a class of 300 students enters all test results in a computer file. A program calculates the following summary statistics: ' midtenn score: average: 57 points, ‘ SD = 18rpoints final score: average = 52 points, SD = 25 points correlation = 0160 The program also runs through the 300 students and calculates for each, regression estimate of final score from midterm score. For some of the students, the regression estimate was off by more than 20 points. About how many? 9. (IOpriints) The histogram below shows the distribution of family income in a small town. The data is hypothetical. ' ' (a) If the density scale is used on the vertical axis, what number belongs at the arrow? _ (b) What are the units for the answer to (a)? . ('c) What percent of the families eamed between $10,000 and $20,000? (d) Is the average income under $40,000, over $40,000 equal to $40,000? Circle your choice and explain your reasoning. (Note: Assume that family income is spread evenly within each of the six class intervals used in the histogram: 0-10, 10-20, 20-30, 30-50, 50-70 and 70-80.) 10. (10 points) (a) What is the correlation coefficient between x and y in the data set below? K Y 15 3 15 17 14 19 12 20 14 20 16 21 ‘19 - 4O ‘ Now: To save you a little time, the sum of the x-column is 105, and the sum of the y-column is 140. - (b) What is the correlation coefficient between x and y in the data set below? _"__..__X__ 15 15 14 12 14 16 19 H-FQCDGMU! 11. (10poims) An aerobics study involved 645 men. The average weight of the men was 166.5 pounds. The histogram of weight followed the normal curve closely. Out of the 645 men, there were 200 men who weighed under 150 pounds. (a) HOW many weighed over 183 pounds? (b) How many weighed under 140 pounds? [2, . (10 points) Agroup .of 100 managers has an average salary of $52,000; the so is $10,000. ’ - 3:333:19, 4O womenin the group. The average of their salaries is also $52,000, but the SD is a D. . I . . (0) Find the .aVerage of'the Jnen’s salaries. (b) Find the SD of the men's salaries. [3 (lOpoims) r A list of numbers has an aVera'ge of40 and an SD of 15. A new list is formed ' - . by adding 10' to every number on the list. If possible, find the r.m.s. of the numbers on the new list. If it is not possible, explain why not. I (5. ohm) The average age of a group of 25 programmers is 28 years. The SD is-4 years. ' 011% member of the group, who is 40, leaves. No-one ishired to replace mm. For the reduced group: - - (3) average age = ' .(b)'SD age: {fl . (10 points) A study is made of the Math and Verbal SAT scores for the entering class at a . certain college. The summary statistics are as follows: average M~SAT=560 SD '= 120 average V-SAT = 520 SD = 110 a correlation coefficient = 0.64 The scatter diagram is football—shaped. (a) Some one who scored 500 on the M-SAT would have a percentile rank (within the entering class) on the M—SAT of . (b) Of all those who scored 500 on the M—SAT, about " percent had a higher percentile rank on the V~SAT than on the M—SAT. [a (5 points) The men enrolled in a large sports medicine course had an average weight of 160 pounds and an SD of 30 pounds. rFheir weights followed the normal curch closely. Consider the men in the course who weighed somewhere between 180 and 200 pounds. The average weight of these men would be: M equal to 190 pounds. bigger than 190 pounds. smaller than 190 pounds. can’t tell without more information. Check (NI) one of the above options. Please explain your choice. r1: ( 5 points) There are 1600 first-year students at a certain university. Their scores on the Verbal SAT followed the normal curve closely, and the average score was 550 points. Around 360 students had scores in the range from 550 to 600 points. How many had scores in the range from 600 to 650 points? I ‘ n . - . . - ' ‘ - b ' . the . ' ' ‘ Th ' vera e of a hat of numbers IS 108. A statistician calculates the r.m.s. o (a higiggggstfiognaflie agerage of the list and gets 5.0. Unfortunately, he happened to misread; to average of the list as 106, and used that instead of 108 when calculating the devrattons. o the SD is not 5.0. Find the correct SD. 1 9- (Spoints) Ten people are in a ' ‘ I ' ’ l l I _ I room, waitlng to be interviewed. There are tWo br ' iglrpup, but these are the only two that are related. The people are called in one atoaflhfirhselIh‘ihbz9 emewed. The choice of who goes next is done at random. , ’ e (a) Find the the;brothers are the first two people to be interviewed. Findth ‘ ' (b) is the flitghance the older brotheris first person to be interwewed and the younger brother 2 O . ( 5 pain-ts) Someone shuffles a deck of cards and dealsouptwo cards. Then he this again with asecond deck of cards. Find the chanc th tth" ' red the two from the second deck are black. 6 a 6 two cards from thc firm deCk am 2 1 . A die is rolled three times. Find the chance that: (a) The three numbers rolled are either all the same or all different. (b) Two of the numbers are the same and the third is different. 22. I( 5 points) Two draws are made at random with replacement from the box: IIIIHEIHEH Frnd the chance the second number is bigger than twice the first one. 2 3 . (5 points) A box contains two red, two white, and one blue marble. Tomorrow, two marbles will be drawn at random, with replacement from the box. Find the chance the second marble is a different color than the first one. For both parts, answer yes or no and explain your answer. Zaf '. (10 points) In a certain game, a player picks a number from 1 to 6 and bets on it. Then a die ' is rolled 4 times. If the player’s number shows up one or more times, the player wins. Otherwise, the player loses. 3th people are playing the game: Oliver bets on 1, Tanya on 2, Thad on 3, Felice on 4, Filene on 5, and Sam on .6. (a) Find the chance-that Sam wins. (in) Find the chance neither Oliver nor Tanya win. (c) Find the chance both Oliver and Tanya win but no one else does. 7,; . '( 5 points) Two cards are dealt from a deck of cards. Find the-chance that neither card is a diamond. (A deck of cards contains 52 cards: 13 spades, 13 hearts, 13 diamonds, and 13 clubs.) 118 at a time, from a deck of cards. Find the chance that the 26” (5 POW-9) Five cards are dealt) 0 d these are the only hearts in the five cards. (YOU ‘10 not _ ‘ I first and fifth cards are hearts, an have to work out the arithmetic.) 2 7 - "(5- points) First one ticket, and then a second one, are drawn at random from the box shown 7. below. The draw-s are-made without replacement. Us ...
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This note was uploaded on 02/08/2011 for the course STAT 21 taught by Professor Anderes during the Fall '08 term at University of California, Berkeley.

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S21MidtermStudyGuide - Hank Ibser Statistics 21 Spring 2010...

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