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1 0_EBAeSolutonsChapter.pdf 0_EBAe Case Soln Chapter.pdf

2 Chapter Solutons: 1. a. Quanttatve b. Categorcal c. Categorcal d. Quanttatve e. Categorcal. a. The top 10 countres accordng to GDP are lsted below. Country Contnent GDP (mllons of US$) Unted States North Amerca 15,094,05 Chna Asa 7,98,147 Japan Asa 5,869,471 Germany Europe 3,577,031 France Europe,776,34 Brazl South Amerca,49,908 Unted Kngdom Europe,417,570 Italy Europe,198,730 Russa Asa 1,850,401 Canada North Amerca 1,736,869 b. The top 5 countres by GDP located n Afrca are lsted below. Country Contnent GDP (mllons of US$) South Afrca Afrca 408,074 Ngera Afrca 38,90 Egypt Afrca 35,719 Algera Afrca 190,709 Angola Afrca 100, a. The sorted lst of carrers appears below. Carrer Prevous Year On-tme Percentage Current Year On-tme Percentage Blue Box Shppng 88.4% 94.8% Cheetah LLC 89.3% 91.8% Smth Logstcs 84.3% 88.7% Grante State Carrers 81.8% 87.6% - 1

3 Super Freght 9.1% 86.8% Mnuteman Company 91.0% 84.% Jones Brothers 68.9% 8.8% Honsn Lmted 74.% 80.1% Rapd Response 78.8% 70.9% Blue Box Shppng s provdng the best on-tme servce n the current year. Rapd Response s provdng the worst on-tme servce n the current year. b. The output from Excel wth condtonal formattng appears below. c. The output from Excel contanng data bars appears below. d. The top 4 shppers based on current year on-tme percentage (Blue Box Shppng, Cheetah LLC, Smth Logstcs, and Grante State Carrers) all have postve ncreases from the prevous year and hgh on-tme percentages. These are good canddates for carrers to use n the future. 4. a. The relatve frequency of D s = 0.0. b. If the total sample sze s 00 the frequency of D s 0.0*00 = 40. c. and d. Class Relatve Frequency Frequency % Frequency A

4 B C D Total a. These data are categorcal. b. % Show Frequency Frequency Jep 9 18 JJ 8 16 BBT 14 8 THM 6 1 WoF 13 6 Total c. The largest vewng audence s for The Bg Bang Theory and the second largest s for Wheel of Fortune. 6. a. Least = 1, Hghest = 3 b. Percent Hours n Meetngs per Week Frequency Frequency % % % % % % % 5 100% - 3

5 Fequency c Hours per Week n Meetngs The dstrbuton s slghtly skewed to the left. 7. a. Industry Frequency % Frequency Bank 6 13% Cable 44 % Car 4 1% Cell 60 30% Collecton 8 14% Total % b. The cellular phone provders had the hghest number of complants. c. The percentage frequency dstrbuton shows that the two fnancal ndustres (banks and collecton agences) had about the same number of complants. Also, new car dealers and cable and satellte televson companes also had about the same number of complants. 8. a. Lvng Area Lve Now Ideal Communty Cty 3/100=3% 4/100=4% Suburb 6/100=6% 5/100=5% Small Town 6/100=6% 30/100=30% Rural Area 16/100=16% 1/100=1% Total 100% 100% - 4

6 Percent Percent Where do you lve now? 35% 30% 5% 0% 15% 10% 5% 0% Cty Suburb Small Town Rural Area Lvng Area What do you consder the deal communty? 35% 30% 5% 0% 15% 10% 5% 0% Cty Suburb Small Town Rural Area Ideal Communty b. Most adults are now lvng n a cty (3%). c. Most adults consder the deal communty a small town (30%). d. Changes n percentages by lvng area: Cty 8%, Suburb 1%, Small Town +4%, and Rural Area +5%. Suburb lvng s steady, but the trend would be that lvng n the cty would declne whle lvng n small towns and rural areas would ncrease. - 5

7 9. a. b. Class Frequency Total: 40 Class Relatve Frequency Percent Frequency % % % % % Total: % a d. Class Class Frequency Cumulatve Frequency Frequency Relatve Frequency Cumulatve Frequency Cumulatve Relatve Frequency Total: e. From the cumulatve relatve frequency dstrbuton, 60% of customers wat 9 mnutes or less. - 6

8 1. a. Class Frequency b. The dstrbuton s slghtly skewed to the rght. c. The most common score for students s between 1400 and No student scored above 00, and only 3 students scored above Only 4 students scored below a. Mean = = 15 or use the Excel functon AVERAGE. 5 To calculate the medan, we arrange the data n ascendng order: Because we have n = 5 values whch s an odd number, the medan s the mddle value whch s 16 or use the Excel functon MEDIAN. b. Because the addtonal data pont, 1, s lower than the mean and medan computed n part a, we expect the mean and medan to decrease. Calculatng the new mean and medan gves us mean = 14.5 and medan = Wthout Excel, to calculate the 0th percentle, we frst arrange the data n ascendng order: The locaton of the pth percentle s gven by the formula L p = p (n + 1) For our date set, L 0 = (8 + 1) = 1.8. Thus, the 0th percentle s 80% of the way between the value n poston 1 and the value n poston. In other words, the 0 th percentle s the value n poston 1 (15) plus 0.80 tme the dfference between the value n poston (0) and poston 1 (15). Therefore, the 0 th percentle s *(0-15) =

9 We can repeat the steps above to calculate the 5th, 65th and 75th percentles. Or usng Excel, we can use the functon PERCENTILE.EXC to get: 5th percentle = th percentle = th percentle = Mean = = or use the Excel functon AVERAGE. 11 To calculate the medan arrange the values n ascendng order Because we have n = 11, an odd number of values, the medan s the mddle value whch s 57 or use the Excel functon MEDIAN. The mode s the most often occurrng value whch s 53 because 53 appears three tmes n the data set, or use the Excel functon MODE.SNGL because there s only a sngle mode n ths data set. 16. To fnd the mean annual growth rate, we must use the geometrc mean. Frst we note that 3500=5000 x x x 1 9, so x1 x x9 =0.700 where x 1, x, are the growth factors for years, 1,, etc. through year 9. n 9 Next, we calculate x g = (x 1 )(x ) (x n ) = 0.70 = So the mean annual growth rate s ( )100% = % 17. For the Stvers mutual fund, 18000=10000 x x x 1 8, so x1 x x8 =1.8 where x 1, x, are the growth factors for years, 1,, etc. through year 8. 8 x n g x1 x x Next, we calculate So the mean annual return for the Stvers mutual fund s ( )100 = 7.64%. For the Trpp mutual fund we have: x1 x x8 x x x, so = x n x x x =.1 and g So the mean annual return for the Trpp mutual fund s ( )100 = 9.848%. Whle the Stvers mutual fund has generated a nce annual return of 7.6%, the annual return of 9.8% earned by the Trpp mutual fund s far superor. - 8

10 Alternatvely, we can use Excel and the functon GEOMEAN as shown below: 18. a. Mean = n =1 x n = = b. To calculate the medan, we frst sort all 48 commute tmes n ascendng order. Because there are an even number of values (48), the medan s between the 4th and 5th largest values. The 4th largest value s 5.8 and the 5th largest value s 6.1. ( )/ = 5.95 Or we can use the Excel functon MEDIAN. c. The values 3.4 and 4.8 both appear three tmes n the data set, so these two values are the modes of the commute tmes. To fnd ths usng Excel, we must use the MODE.MULT functon. d. Standard devaton = In Excel, we can fnd ths value usng the functon STDEV.S. Varance = = In Excel, we can fnd ths value usng the functon VAR.S. e. The thrd quartle s the 75th percentle of the data. To fnd the 75th percentle wthout Excel, we frst arrange the data n ascendng order. Next we calculate L p = p (n + 1) = L = 75 (48 + 1) = In other words, ths value s 75% of the way between the 36 th and 37 th postons. However, n our date the values n both the 36 th and 37 th postons are 8.5. Therefore, the 75th percentle s 8.5. Or usng Excel, we can use the functon PERCENTILE.EXC. 19. a. The mean watng tme for patents wth the wat-trackng system s 17. mnutes and the medan watng tme s 13.5 mnutes. The mean watng tme for patents wthout the wat-trackng system s 9.1 mnutes and the medan s 3.5 mnutes. b. The standard devaton of watng tme for patents wth the wat-trackng system s 9.8 and the varance s The standard devaton of watng tme for patents wthout the wat-trackng system s and the varance s

11 c and d. e. Wat tmes for patents wth the wat-trackng system are substantally shorter than those for patents wthout the wat-trackng system. However, some patents wth the wat-trackng system stll experence long wats. 0. a. The medan number of hours worked for scence teachers s 54. b. The medan number of hours worked for Englsh teachers s 47. c. d. - 10

12 e. The box plots show that scence teachers spend more hours workng per week than Englsh teachers. The box plot for scence teachers also shows that most scence teachers work about the same amount of hours; n other words, there s less varablty n the number of hours worked for scence teachers. 1. a. Recall that the mean patent wat tme wthout wat-tme trackng s 9.1 and the standard devaton of wat tmes s Then the z-score s calculated as, z = = b. Recall that the mean patent wat tme wth wat-tme trackng s 17. and the standard devaton of wat tmes s 9.8. Then the z-score s calculated as, z = = As ndcated by the postve z scores, both patents had wat tmes that exceeded the means of ther respectve samples. Even though the patents had the same wat tme, the z score for the sxth patent n the sample who vsted an offce wth a wat trackng system s much larger because that patent s part of a sample wth a smaller mean and a smaller standard devaton. c. To calculate the z-score for each patent watng tme, we can use the formula z = x x or we can use s the Excel functon STANDARDIZE. The z scores for all patents follow. Wthout Wat-Trackng System 16.6 Wth Wat-Trackng System Wat Tme z-score Wat Tme z-score

13 y No z-score s less than -3.0 or above +3.0; therefore, the z scores do not ndcate the exstence of any outlers n ether sample.. a. Accordng to the emprcal rule, approxmately 95% of data values wll be wthn two standard devatons of the mean. 4.5 s two standard devaton less than the mean and 9.3 s two standard devatons greater than the mean. Therefore, approxmately 95% of ndvduals sleep between 4.5 and 9.3 hours per nght. b. z = = c. z = = a. 615 s one standard devaton above the mean. The emprcal rule states that 68% of data values wll be wthn one standard devaton of the mean. Because a bell-shaped dstrbuton s symmetrc half of the remanng values wll be greater than the (mean + 1 standard devaton) and half wll be below (mean 1 standard devaton). In other words, we expect that 0.5*(1-68%) = 16% of the data values wll be greater than (mean + 1 standard devaton) = 615. b. 715 s two standard devatons above the mean. The emprcal rule states that 95% of data values wll be wthn two standard devatons of the mean, and we expect that 0.5*(1-95%) =.5% of data values wll be above two standard devatons above the mean. c. 415 s one standard devaton below the mean. The emprcal rule states that 68% of data values wll be wthn one standard devaton of the mean, and we expect that 0.5*(1-68%) = 16% of data values wll be below one standard devaton below the mean. 515 s the mean, so we expect that 50% of the data values wll be below the mean. Therefore, we expect 50% - 16% = 36% of the data values wll be between the mean and one standard devaton below the mean (between 414 and 515). d. z = e. z = = 1.05 = a x b. There appears to be a negatve lnear relatonshp between the x and y varables. - 1

14 c. Wthout Excel, we can use the calculatons shown below to calculate the covarance: x y (x x ) (y y ) ( x x)( y y) x = 8 y = 46 s xy = (x x )(y y ) n 1 = = 60 Or, usng Excel, we can use the COVARIANCE.S functon. The negatve covarance confrms that there s a negatve lnear relatonshp between the x and y varables n ths data set. d. To calculate the correlaton coeffcent wthout Excel, we need the standard devaton for x and y: s x = 5.43, s y = Then the correlaton coeffcent s calculated as: r xy = s xy 60 = = s x s y (5.43)(11.40) Or we can use the Excel functon CORREL. The correlaton coeffcent ndcates a strong negatve lnear assocaton between the x and y varables n ths data set. 5. a. The scatter chart ndcates that there may be a postve lnear relatonshp between profts and market captalzaton. b. Wthout Excel, we can use the calculatons below to fnd the covarance and correlaton coeffcent: x y ( x x) ( y y) ( x x) y ( x x)( y y) ( y ) , , , , , , , ,

15 3, , , , , , Total s xy = (x x )(y y ) n 1 s x = (x x ) n 1 = = = = (y y ) s y = = = n 1 30 r xy = s xy = s x s y ( )( ) = 0.89 Or usng Excel, we use the formula = COVARIANCE.S(B:B3,C:C3) to calculate the covarance, whch s Ths ndcates that there s a postve relatonshp between profts and market captalzaton. c. In the Excel fle, we use the formula =CORREL(B:B3,C:C3) to calculate the correlaton coeffcent, whch s Ths ndcates that there s a strong lnear relatonshp between profts and market captalzaton. 6. a. Wthout Excel, we can use the calculatons below to fnd the correlaton coeffcent: x y ( x x) ( y y) ( x x) y ( x x)( y y) ( y )

16 Delnquent Loans (%) Total s xy = (x x )(y y ) n 1 s x = (x x ) n 1 Or we can use the Excel functon CORREL. = = = = (y y ) s y = = =.366 n 1 6 r xy = s xy = s x s y (0.9956)(.366) = 0.44 The correlaton coeffcent ndcates that there s a moderate postve lnear relatonshp between jobless rate and delnquent loans. If the jobless rate were to ncrease, t s lkely that an ncrease n the percentage of delnquent housng loans would also occur. b Jobless Rate (%) - 15

17 Frequency Chapter Case Problem: Heavenly Chocolates Webste Traffc 1. Descrptve statstcs for the tme spent on the webste, number of pages vewed, and amount spent are shown below. Tme (mn) Pages Vewed Amount Spent ($) Mean Medan Standard Devaton Range Mnmum Maxmum Sum The mean tme a shopper s on the Heavenly Chocolates webste s 1.8 mnutes, wth a mnmum tme of 4.3 mnutes and a maxmum tme of 3.9 mnutes. The followng hstogram demonstrates that the data are skewed to the rght. 14 Hstogram of Tme (mn) Tme (mn) 5 30 The mean number of pages vewed durng a vst s 4.8 pages wth a mnmun of pages and a maxmum of 10 pages A hstogram of the number of pages vewed ndcates that the data are slghtly skewed to the rght.

18 Frequency Frequency Solutons to Case Problems Hstogram of Pages Vewed Pages Vewed 8 10 The mean amount spent for an on-lne shopper s $68.13 wth a mnmum amount spent of $17.84 and a maxmum amount spent of $ The followng hstogram ndcates that the data are skewed to the rght. 10 Hstogram of Amount Amount Summary by Day of Week Day of Week Frequency Total Amount Spent ($) Average Amount Spent ($) Sunday Monday Tuesday Wednesday Thursday Frday Saturday Total

19 The above summary shows that Monday and Frday are the best days n terms of both the total amount spent and the averge amount spent per transacton. Frday had the most purchases (11) and the hghest value for total amount spent ($945.43). Monday, wth nne transactons, had the hghest average amount spent per transacton ($90.38). Sunday was the worst sales day of the week n terms of number of transactons (5), total amount spent ($18.15), and average amount spent per transacton ($43.63). However, the sample sze for each day of the week are very small, wth only Frday havng more than ten transactons. We would suggest a larger sample sze be taken before recommendng any specfc stratgegy based on the day of week statstcs. 3. Summary by Type of Browser Browser Frequency Total Amount Spent ($) Average Amount Spent ($) Frefox Chrome Other Chrome was used by 7 of the 50 shoppers (54%). But, the average amount spent spent by customers who used Chrome ($61.36) s less than the average amount spent by customers who used Frefox ($76.76) or some other type of browser ($74.48). Ths result would suggest targetng specal promoton offers to Frefox users or users of other types of browsers. But, before recommendng any specfc strateges based upon the type of browser, we would suggest takng a larger smaple sze. 4. A scatter dagram showng the relatonshp between tme spent on the webste and the amount spent follows: The sample correlaton coeffcent between these two varables s.580. The scatter dagram and the sample correlaton coeffcent ndcate a postve relatonshp between tme spent on the webste and the total amount spent. Thus, the sample data support the concluson that customers who spend more tme on the webste spend more. 5. A scatter dagram showng the relatonshp between the number of pages vewed and the amount spent follows:

20 Solutons to Case Problems The sample correlaton coeffcent between these two varables s.74. The scatter dagram and the sample correlaton coeffcent ndcate a postve relatonshp between tme spent on the webste and the number of pages vewed. Thus, the sample data support the concluson that customers who vew more webste pages spend more. 6. A scatter dagram showng the relatonshp between the number of pages vewed and the tme spent on the webste follows: The sample correlaton coeffcent between these two varables s.596. The scatter dagram and the sample correlaton coeffcent ndcate a postve relatonshp between the number of pages vewed and the tme spent on the webste. Summary: The analyss ndcates that on-lne shoppers who spend more tme on the company s webste and/or vew more webste pages spend more money durng ther vst to the webste. If Heavenly Chocolates can develop an attractve webste such that on-lne shoppers are wllng to spend more tme on the webste and/or vew more pages, there s a good possblty that the company wll experence greater sales. And, consderaton should also be gven to developng marketng strateges based upon possble dfferences n sales assocated wth the day of the week as well as dfferences n sales assocated wth the type of browser used by the customer.

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