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Exam 1 ECN 221 Chapter 2 What type of data (categorical, discrete numerical, or continuous numerical) is each of the following variables? Continuous numerical @ (b) Number of peanuts in a can of Planter’s Mixed Nuts. Discrete numerical @ (c) Occupation of a mortgage applicant. Categorical o Continuous_ numerical @ (a) Length of a TV commercial. (d) Flight time from London Heathrow to Chicago O'Hare. What type of data (categorical, discrete numerical, or continuous numerical) is each of the following variables? (a) The manufacturer of your car. Categorical o (b) Your college major. Categorical °o (c) The number of college credits you are taking. Discrete numerical @ Continuous Numerical: Values that can take on any real numbers including decimals. Measured not counted. Discrete Numerical: Values based on observations that can be counted. Usually takes on whole numbers. Categorical: Labels or names used to identify an attribute of each element. Categorical data use either the nominal or ordinal scale of measurement and may be nonnumeric or numeric Below is a6 * 8 array containing the ages of moviegoers. Treat this as a population. 32 34 33 12 57 13 58 16 23 23 62 65 35 15 Ae 20 14 pl 51 33 31 13 AL: 58 23 10 63 34 12: 15 62 13 40 a1 18 62 64 30 42 20 21; 56 11 51 38 49 ss) 21 (a) What was the proportion of all 48 moviegoers who were under age 30? (Round your answer to 2 decimal places.) Proportion 0.50 9 Which type of data (categorical, discrete numerical, continuous numerical) is each of the following variables? (a) Number of spectators at a randomly chosen Wimbledon tennis match. Discrete numerical 9 (b) Water consumption (liters) by a randomly chosen Wimbledon player during a match. Continuous numerical (c) Gender of a randomly chosen tennis player in the Wimbledon tennis tournament. Categorical °o Would you use a sample or a census to measure each of the following? (a) The number of cans of Campbell's soup on your local supermarket's shelf today at 6:00p.m. Census @ (b) The proportion of soup sales last week in Boston that was sold under the Campbell's brand. Sample @ (c) The proportion of Campbell's brand soup cans in your family's pantry. Census 9 Would you use a sample or census ta measure each of the following? (a) The number of workers currently employed by Campbell Soup Company. Census @ (b) The average price of a can of Campbell's Cream of Mushroom soup. Sample oO (c) The total earnings of workers employed by Campbell Soup Company last year. Census @ There are 327 official ports of entry in the United States. The Department of Homeland Security selects 15 ports of entry at random to be audited for compliance with screening procedures of incoming travelers through the primary and secondary vehicle and pedestrian lanes. What kind of sample is this? Stratified sample Cluster sample Systematic sample Which survey questions below would be sultable for a set of check boxes providing cholces for the respondent to choose from? (You may select more than one answer.) How concerned are you for the environment? What company do you work for? What was the amount of your last utility bill? A tabletop survey by a restaurant asked the question shown below. Classic systematic sample from an accessible but unlisted population. Sampling bias can best be reduced by: using appropriate data coding. havin ; acom a tabulate the results. taking a judgment sample. Sampling error can't be eliminated, but sampling bias can be avoided. Chapter 4 PP Prof. Hardtack gave four Friday quizzes last semester in his 10-student senior tax accounting class. Quiz 1: 60, 60, 60, 60, 71, 73, 74, 75, 88, 99 Quiz 2: 65, 65, 65, 65, 70, 74, 79, 79, 79, 79 Quiz 3: 66, 67, 70, 71, 72, 72, 74, 74, 95, 99 Quiz 4: 10, 49, 70, 80, 85, 88, 90, 93, 97, 98 & Click here for the Excel Data File (a) Find the mean, median, and mode for each Quiz. (Leave no cells blank - be certain to select "None" wherever required. Round your answers to 2 decimal places.) Quiz 1 Quiz 2 Count 10.00 O 10.00 9 Mean 72.00 @ 72.00 9 Median 72.00 @ 72.00 @ Mode 609 65,790 (b) Do these measures of center agree? No @ Quiz 3 10.00 9 76.00 72.00 @ 72,749 Quiz 4 10.00 0 76.00 86.50 0 None @ (c) For each data set, note strengths or weaknesses of each statistic of center. (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.) Where the mean and median disagree, one should look at the shape of the distribution to see which measure is more appropriate. The mode is a reliable measure of central tendency for quantitative data. Where the mean and median agree, one should look at the shape of the distribution to see which measure is more appropriate. The mode is an unreliable measure of central tendency for quantitative data. (d)Are the data symmetric or skewed? If skewed, which direction? Quiz1 Symmetric @ Quiz 2 Symmetric ° Quiz3 Skewed right O Quiz4 Skewed left (e) Pick the correct student performance on each Quiz. Students on average did better on: Quizzes 3 and 4. 9 Following are the three types of data sets: a. Exam scores (9 students) 42, 55, 65, 67, 68, 75, 76, 78, 94 b. GPAs (8 students) 2.25, 2.55, 2.95, 3.02, 3.04, 3.37, 3.51, 3.66 c. Class absences (12 students) 0, 0, 0, 0, 0, 1, 2, 3, 3, 5, 5, Beciick here for the Excel Data File For each data set, find the median, midrange, and geometric mean. (Round your answers to 2 decimal places. Leave no cells blank. Enter "0" as an answer if undefined.) a b c Median 68.00 @ 3.03 O 1.50 0 Midrange 68.00 @ 3.00 O 7.50 O Geometric mean 67.37 @ 3.04 @ 09 Exercise 4-27 Stock A: X"""X” = $24.50, s = 5.25 Stock B: X~"X” = $147.25, s = 12.25 Stock C: X"""X~ = $5.75, s = 2.08 (a) Find the coefficient of variation for prices of these three stocks. (Round your answers to 2 decimal places.) Coefficient of Shes variation Stock A 21.43 9% Stock B 3.32 O% Stock C 36.17 9% (b) Which stock has the greatest relative variation? [& click here for the Excel Data File (a) Use Excel to find the quartiles. ist quartile Median 3rd quartile Interquartile range (b) Find the midhinge. Midhinge 39 Section Exercise 4-48 For each X-Y data set (n = 12): Data Set (a) X 64.7 25.9 656 49.6 503 Y 58 181 106 119 114 Data Set (b) X 55.1 59.8 723 864 311 Y a5 175 152 206 7:2 Data Set (c) X 53.3 18.1 498 43.8 68.3 Y 102 69 148 134 168 & Click here for the Excel Data File 1.00 9 2.00 O 5.00 O 4.00 9 26.7 39.5 146 15.7 41.8 40.7 30.4 18.6 95 163 (a) Match the data sets to the scatter plots below. 56.0 44 36.8 8.2 45.8 16.4 90.8 42.7 a3-7 34.0 15 35.9 15.4 28.9 AT? 56.7 11.4 39.9 14.7 24.8 60.3 10.9 29.3 19.7 20.0 7 15.0 po > 10.0 * ¢ 5:0 * o 0.0 +—+ +—}—_+—_+—_+_ ++] 20.0 70.0 120.0 x Data Set (a) 9 25.0 20.0 rs ; 15.0 bs a = 40.0 ; 7 50+ ° 0.0 +++% + +—+—+—+—_ +] 0.0 50.0 100.0 x Data Set (c) 9 Mean Standard Coefficient of Investment Return Deviation Variation Venture funds (adjusted) 19.2 14.0 72.92 O% All common stocks 15.6 14.0 29.74 O% Real estate 11.5 16.8 146.09 Ox Federal short-term paper 6.7 19 28.36 O% (b) Why would we use a coefficient of variation, and why not just compare the standard deviations? The standard deviations are an "absolute" not relative measure of dispersion. It is best to use the CV when comparing across variables that have different means. @ (c) What do the data tell you about risk and return at that time period? enture fund on the cv. 0 Section Exercise 4-37 a. Student GPAs: Bob's z-score Zz = +171 Wy =298 Oo = 036 b. Weekly work hours: Sarah's z-score Zz = +118 Wy =216 Oa = 7.1 c. Bowling scores: Dave's z-score Z = -135 My = 150 Oo = 40 Find the original data value corresponding to each standardized z-score. (Round your answers to 2 decimal places.) a. Bob's GPA 3.60 0 b. Sarah's weekly work hours. 29.98 © c. Dave's bowling score 96.00 9 Section Exercise 4-38 CitiBank recorded the number of customers to use a downtown ATM during the noon hour on 32 consecutive workdays. 25 37 23 26 30 40 25 26 39 32 21 26 19 27 32 25 18 26 34 #18 #31 35 21 33 33 9 16 32 35 42 15 24 [& Click here for the Excel Data File (a)Use Excel or MegaStat to sort and standardize the data. What is the z-score for the following x value? (Round your answer to 2 decimal places. A negative amount should be indicated by a minus sign.) x value z-score 21 -0.81 0 (b) Based on the Empirical Rule, are there outliers? No @ (c) What percent of the data fall within 1 standard deviation of the mean? Within 2 standard deviations of the mean? (Round your answers to 2 decimal places. Omit the “%” sign in your response.) Empirical Rule Mean — (1*s) 19.49 O Mean + (1*s) 35.20 O Percent in interval (68.26%) 68.75 9 % Mean — (2*s) 11.64 O Mean + (2*s) 43.05 O Percent in interval (95.44%) 96.88 O % Chapter 5 PP Adie is thrown (1, 2, 3, 4, 5, 6) and a coin is tossed (H, T). (a) Choose the sample space for the die/coin combination for the elementary events given. S = {(L.H), (2,4), (3,4), (4,4), (5.4), (6,4), (1,7), (2,7), (3,7), (4.7), (5,7) (6,.7)} 8 (b) Are the elementary events equally likely? Yes 9 Given P(A) = 0.70, P(B) = 0.30, and P(A n B) = 0.00: (a) Find P(A U B). P(A U B) 1.00 8 18-34 39 30 69 35-54 10 10 20 55+ 3 8 a1. Column Total 52 48 100 Find the following probabilities or percentages: (a) Probability that a viewer is aged 18-34. Probability 0.6900 @ 69/100=0.69 (b) Probability that a viewer prefers watching TV videos. Probability 0.4800 @ 48/100=0.48 (c) Percentage of viewers who are 18-34 and prefer watching user-created videos. Percentage of viewers 399% 39/100 (d) Percentage of viewers aged 18-34 who prefer watching user-created videos. (Round your answer to 2 decimal places.) Percentage of viewers 57.00 8 % 39/69=57 (e) Percentage of viewers who are 35-54 or prefer user-created videos. Percentage of viewers 629% 10+10+39+3/100=62% This contingency table describes 200 business students. Major Gender Accounting(A) Economics(E) — Statistics(S) Row Total Female(F) 44 30 24 98 Male(M) 56 30 16 102 Gann 100 60 40 200 Total & Click here for the Excel Data File Find each probability (Round your answers to 4 decimal places.) 3 Pa) 0.5000 @ ® pu 0.5100 @ c. P(A 1 M) 0.2800 9 la PIF nS) 0.1200 9 ° PIM) 0.5500 © f. PALF) 0.4500 O 9 PFS) 0.6000 @ " PEUA 0.6400 O How to get answers A: 100/200=0.5 B 102/200=0.51 C. 56/200=0.28 D. 24/200=0.12 E. 56/102=0.55 F. 44/98=0.45 G.24/40=0.6 H. 60/200+98/200-30/200=0.64 This contingency table shows average yield (rows) and average duration (columns) for 38 bond funds. Average Portfolio Duration Intermediate(D Yield Short(D:) ) Long(D;) Row Total Small(¥;) 8 2 0 10 Medium(Y,) al 6 6 13 High(Y2) 2 4 9 15 Column Total 11 12 15 38 & Click here for the Excel Data File For a randomly chosen bond fund, find the probability of the following: (Round your answers to 4 decimal places.) a.The bond fund is long duration. 0.3947 O b. The bond fund has high yield. 0.3947 O c. The bond fund has high yield given that it is of short duration. 0.1818 O d.The bond fund is of short duration given that it has high yield. 0.1333 O -687 This is a conditional probability: P(W | M) = 18/31. From the following tree, find the probability that a randomly chosen person will get the flu. 70 -30 07 81 -70 Multiply down two branches and add .07 to .12. That is (.70)(.10) + (.30)(.40). Given the contingency table shown here, find P(A:). Ai A a Ay B 12 26 ) 68 B, 14 28 4 64 By 18 32 47 N22 Col Total 4 86 133 204 .1766 .8163 .0578 This is a marginal probability: P(A) = 86/467. Row Total 148 150 169 467 Given the contingency table shown here, find P(A> | Bs). A, Az Ay Ay Row Total By 2 | 2 2 68 148 B; I4 28 +H 64 150 By 1s 32 47 72 169 Col Total 44 86 133 204 467 .0685 1893 3721 1842 This is a conditional probability: P(A2|B;) = 32/169. The mean of a population is 50 and the median is 40. Which histogram is most likely for samples from this population? A B c Sample B. Sample C. Mean exceeds median so skewed right. Definition: Left-skewed: Median larger than the mean. Right-skewed: Median less than the mean 
