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business
business statistics in practice
Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions
=+67. Hurricanes. Buying insurance for property loss from hurricanes has become increasingly difficult since Hurricane Katrina caused record property loss damage. Many companies have refused to renew policies or write new ones. The data set provided contains the total number of hurricanes by every
=+66. ZIP codes. Holes-R-Us, an Internet company that sells piercing jewelry, keeps transaction records on its sales. At a recent sales meeting, one of the staff presented the following histogram and summary statistics of the ZIP codes of the last 500 customers, so that the staff might understand
=+b) What advice might you give the analyst about the appropriateness of this display?0 70440000 70500000 70560000 ID 70620000 70680000 24 68 10 Frequency 12 14
=+a) What might account for the distribution seen in the histogram?
=+65. Houses for sale. Each house listed on the multiple listing service (MLS) is assigned a sequential ID number. A recently hired real estate agent decided to examine the MLS numbers in a recent random sample of homes for sale by one real estate agency in nearby towns. To begin the analysis,
=+64. Importance of pay. Using data from the World Values Survey project, we can investigate how culturally important it is to have job that pays well. Compare the importance of a well-paying job for the nine cultural regions using an appropriate display and write a brief summary of the
=+63. Respected jobs. Values, in general, do have a cultural aspect. Using the World Values Survey project data, we can investigate how important it is for a person to have a respected job. Compare the importance of a respected job for the nine cultural regions using an appropriate display and
=+b) What advice might you give the analyst about the appropriateness of this display?
=+a) What might account for the gaps seen in the histogram?
=+62. CEOs. For each CEO, a code is listed that corresponds to the industry of the CEO’s company. Here are a few of the codes and the industries to which they correspond:Industry Industry Code Industry Industry Code Financial services 1 Energy 12 Food/drink/tobacco 2 Capital goods 14 Health 3
=+c) Is that why these are so different?
=+b) What are the typical reasons that cause measures of center and spread to be as different as those in this table?
=+a) What does the mean of 54.41 mean?
=+An intern who was asked to analyze the organization’s fundraising efforts presented these summary statistics for the variable Title.Mean 54.41 StdDev 957.62 Median 1 IQR 2 n 94,649
=+61. Customer database. A philanthropic organization has a database of millions of donors that they contact by mail to raise money for charities. One of the variables in the database, Title, contains the title of the person or persons printed on the address label. The most common are Mr., Ms.,
=+Write a report summarizing the findings of the investigation.Include appropriate visual and verbal displays of the distributions, and make a recommendation to the agent about the average premium that a fireplace is worth in this market.
=+60. Fire sale. A real estate agent notices that houses with fireplaces often fetch a premium in the market and wants to assess the difference in sales price of 60 homes that recently sold. The data and summary are shown in the table.No Fireplace Fireplace 142,212 134,865 206,512 118,007 50,709
=+Write a report summarizing the findings of the experiment. Include appropriate visual and verbal displays of the distributions, and make a recommendation to the engineers if they are most interested in the accuracy of the method.M03_SHAR8696_03_SE_C03.indd 119 14/07/14 7:27 AM 120 CHAPTER 3
=+59. Quality control holes. Engineers at a computer production plant tested two methods for accuracy in drilling holes into a PC board. They tested how fast they could set the drilling machine by running 10 boards at each of two different speeds. To assess the results, they measured the distance
=+58. Test scores, again. Look again at the histograms of test scores for the three Statistics classes in Exercise 57.a) Overall, which class do you think performed better on the test? Why?b) How would you describe the shape of each distribution?c) Match each class with the corresponding boxplot.20
=+e) Which class had the smallest IQR?
=+d) Which class had the smallest standard deviation?
=+c) For which class are the mean and median most different? Which is higher? Why?
=+57. Test scores. Three Statistics classes all took the same test. Here are histograms of the scores for each class. # of Students 30 60 90 24 6Class 1# of Students 30 60 90 12 34 5Class 2# of Students 30 60 90 24 68 Class 3a) Which class had the highest mean score?b) Which class had the highest
=+56. Mutual funds, historical. Here is an ogive of the distribution of monthly returns for a group of aggressive (or high growth) mutual funds over a period of 25 years. (Recall from Exercise 55 that an ogive, or cumulative relative frequency graph, shows the percent of cases at or below a
=+b) Estimate the quartiles.c) Estimate the range and the IQR.d) Create a boxplot of these speeds.e) Write a few sentences about the speeds of the Kentucky Derby winners.M03_SHAR8696_03_SE_C03.indd 118 14/07/14 7:27 AM Exercises 119
=+55. Derby speeds. How fast do horses run? Kentucky Derby winners top 30 mph, as shown in the graph. This graph shows the percentage of Kentucky Derby winners that have run slower than a given speed. Note that few have won running less than 33 mph, but about 95% of the winning horses have run less
=+e) Write a report on the annual patterns you see in the ozone levels.
=+a) In what month was the highest ozone level ever recorded?b) Which month has the largest IQR?c) Which month has the smallest range?d) Write a brief comparison of the ozone levels in January and June.
=+54. Ozone. Historic ozone levels (in parts per billion, ppb)were recorded at sites in New Jersey monthly. Here are boxplots of the data for each month (over 46 years) lined up in order (January = 1).280 320 360 400 440 1 2 3 4 5 6 7 8 9 10 11 12 Month Ozone (ppb)
=+53. Wine prices 2013. The boxplots display bottle prices (in dollars) of dry Riesling wines produced by vineyards along three of the Finger Lakes in upstate New York.15 10 20 25 30 Cayuga Keuka Seneca Region Pricea) Which lake region produced the most expensive wine?b) Which lake region produced
=+52. Fuel economy. American automobile companies are becoming more motivated to improve the fuel efficiency of the automobiles they produce. It is well known that fuel efficiency is impacted by many characteristics of the car.Describe what these boxplots tell you about the relationship between
=+51. Gas prices 2012. A driver has recorded and posted on the Internet (www.randomuseless.info/gasprice/gasprice.html) the price he paid for gasoline at every purchase from 1979 to 2012. Since 1984 all purchases were self-serve and all were for premium (92-93 octane) gas. He has also standardized
=+50. Unemployment 2012. The data set provided contains 2012(2nd quarter) unemployment rates for 34 developed countries (www.oecd.org). Produce an appropriate graphical display and briefly describe the distribution of unemployment rates. Report and comment on any outliers you may see.
=+49. iPod failures. In the early days of the iPod, MacInTouch(www.macintouch.com/reliability/ipodfailures.html) surveyed readers about reliability. Of the 8926 iPods owned at that time, 7510 were problem-free while the other 1416 failed. From the data on the CD, compute the failure rate for each
=+would you expect the mean, median, standard deviation, and IQR to change?
=+these measures might do a better job of summarizing the spread in the company’s profits? Why?f) If we were to remove the outliers from the data, how
=+d) Summarize the spread of the profit distribution with a standard deviation and with an IQR.e) Given what you know about the distribution, which of
=+these measures might do a better job of summarizing the company’s profits? Why?
=+a) Make a suitable display of the profits from the data provided.b) Summarize the central value for the profits with a median and mean. Why do they differ?c) Given what you know about the distribution, which of
=+48. Insurance profits. Insurance companies don’t know whether a policy they’ve written is profitable until the policy matures (expires). To see how they’ve performed recently, an analyst looked at mature policies and investigated the net profit to the company (in $).
=+f) If we were to remove the outliers from the data, how would you expect the mean, median, standard deviation, and IQR to change?
=+e) Given what you know about the distribution, which of these measures does the better job of summarizing the spread of stores’ sales? Why?
=+d) Summarize the spread of the sales distribution with a standard deviation and with an IQR.
=+c) Given what you know about the distribution, which of these measures does the better job of summarizing the stores’ sales? Why?
=+b) Summarize the central value for sales for this week with a median and mean. Why do they differ?
=+a) Make a suitable display of the sales from the data provided.
=+47. Food sales. Sales (in $) for one week were collected for 18 stores in a food store chain in the northeastern United States. The stores and the towns they are located in vary in size.
=+d) Write a brief description of these data (shape, center, and spread).
=+c) What summary statistics would you use to describe these data?
=+b) Between what sizes do the central 50% of these houses lie?
=+a) What is the range of these sizes?
=+46. Real estate. A real estate agent has surveyed houses in 20 nearby ZIP codes in an attempt to put together a comparison for a new property that she would like to put on the market. She knows that the size of the living area of a house is a strong factor in the price, and she’d like to
=+d) Write a brief description of these data (shape, center, and spread).
=+c) What summary statistics would you use to describe these data?
=+b) Between what lengths do the central 50% of these courses lie?
=+a) What is the range of these lengths?
=+45. Golf courses. A start-up company is planning to build a new golf course. For marketing purposes, the company would like to be able to advertise the new course as one of the more difficult courses in the state of Vermont. One measure of the difficulty of a golf course is its length: the total
=+44. OECD 2011. Established in Paris in 1961, the Organisation for Economic Co-operation and Development(OECD) (www.oecd.org) collects information on many economic and social aspects of countries around the world.Here are the 2011 GDP growth rates (in percentages) of 35 industrialized countries.
=+Australia 519 Korea 541 Austria 487 Luxembourg 482 Belgium 509 Mexico 420 Canada 527 Netherlands 519 Chile 439 New Zealand 524 Czech Republic 490 Norway 500 Denmark 499 Poland 501 Estonia 514 Portugal 490 Finland 543 Slovak Republic 488 France 497 Slovenia 499 Germany 510 Spain 484 Greece 473
=+43. Student skills. Student skills relevant for the labor market contribute to a country’s level of well-being, according to the OECD’s 2013 How’s life? study. Higher skill levels lead to better well-being. The following data show the scores for student skills in 2013 for the OECD
=+e) Describe any unusual observations.
=+d) Describe the shape (center and spread) of this distribution.
=+c) Create a boxplot for these data.
=+42. Pizza prices, part 2. The weekly prices of one brand of frozen pizza over a three-year period in Chicago are provided in the data file. Use the price data to answer the following questions.a) Find the five-number summary for these data.b) Find the range and IQR for these data.
=+41. Pizza prices. The weekly prices of one brand of frozen pizza over a three-year period in Dallas are provided in the data file. Use the price data to answer the following questions.a) Find the five-number summary for these data.b) Find the range and IQR for these data.c) Create a boxplot for
=+d) A student was asked to make a histogram of the data in Exercise 38 and produced the following. Comment.30 40 50 60 70 20 10 0Home Runs 1986 1988 1990 1992 1994 1996 1998 2000 Year
=+c) Without actually finding the mean, would you expect it to be lower or higher than the median? Explain.
=+b) Find the median.
=+a) Would you use the mean or the median to summarize the center of this distribution? Why?
=+40. McGwire, again. Look once more at data of home runs hit by Mark McGwire during his 16-year career as seen in Exercise 38.
=+c) A student was asked to make a histogram of the data in Exercise 33 and produced the following. Comment.80 60 40 20 01979 1981 1983 1985 1987 1989 1991 1993 1995 1997 Year Games Played
=+b) Without actually finding the mean, would you expect it to be lower or higher than the median? Explain.
=+a) Would you use the mean or the median to summarize the center of this distribution? Why?
=+39. Gretzky returns. Look once more at data of hockey games played each season by Wayne Gretzky, seen in Exercise 37.
=+What might explain this?
=+d) What unusual features do you see in this distribution?
=+c) Briefly describe this distribution.
=+38. McGwire. In his 16-year career as a player in major league baseball, Mark McGwire hit 583 home runs, placing him eighth on the all-time home run list (as of 2008).Here are the number of home runs that McGwire hit for each year from 1986 through 2001:3, 49, 32, 33, 39, 22, 42, 9, 9, 39, 52,
=+What might explain this?
=+d) What unusual features do you see in this distribution?
=+37. Gretzky. During his 20 seasons in the National Hockey League, Wayne Gretzky scored 50% more points than anyone else who ever played professional hockey. He accomplished this amazing feat while playing in 280 fewer games than Gordie Howe, the previous record holder.Here are the number of
=+*36. Gas prices 2013, again. The data set provided contains the data from Exercise 30 on the price of gas for 55 stations around San Francisco in January 2013. Create a stem-andleaf display of the data. Point out any unusual features of the data that you can see from the stem-and-leaf.
=+*35. Vineyards. The data set provided contains the data from Exercises 10 and 15. Create a stem-and-leaf display of the sizes of the vineyards in acres. Point out any unusual features of the data that you can see from the stem-andleaf.
=+c) What can you see, if anything, in the histogram of Exercise 32 that isn’t clear in the boxplot?
=+b) Create a boxplot for these data.
=+34. Car discounts, part 2. Use the data set of Exercise 32 to answer the following questions.a) Find the five-number summary for these data.
=+d) What can you see, if anything, in the histogram that isn’t clear in the boxplot?M03_SHAR8696_03_SE_C03.indd 114 14/07/14 7:27 AM Exercises 115
=+c) Create a boxplot for these data.
=+33. Mutual funds 2013, part 2. Use the actual data set of Exercise 31 to answer the following questions.a) Find the five-number summary for these data.b) Find appropriate measures of center and spread for these data.
=+32. Car discounts. A researcher, interested in studying gender differences in negotiations, collects data on the prices that men and women pay for new cars. Here is a histogram of the discounts (the amount in $ below the list price) that men and women received at one car dealership for the last
=+b) In general, how did these funds perform compared to the S&P 500?
=+a) From the histogram, give a short summary of the distribution (shape, center, spread, unusual features).
=+31. Mutual funds 2013. In 2013, the Standard & Poor’s(S&P) 500 stock index reached a new all time high in early April. For the first quarter of 2013, the index was up 10.0%. Here is a histogram of the returns for Money Magazine’s top 70 mutual funds for the same period
=+30. Gas prices 2013. The website LosAngelesGasPrices.com has current gasoline prices all over the United States. In the week of February 5, 2013, the following histogram shows the gas prices at 55 stations in the San Francisco Bay Area. Describe the shape of this distribution (shape, center,
=+c) If both primary and high school take six years in most countries, how many years of higher education do inhabitants of the OECD countries enjoy?
=+b) Which two bins hold the most values for years of education?
=+29. Years in education. According to the OECD’s 2013 How’s life? study, the longer a person has been educated, the higher their well-being. The following histogram shows the distribution of years of education for 34 OECD countries, Russia, and Brazil.14 15 16 17 18 19 20 Count 02 46 810 12 14
=+d) Does the article accurately describe and interpret the data? Explain.M03_SHAR8696_03_SE_C03.indd 113 14/07/14 7:27 AM 114 CHAPTER 3 Displaying and Describing Quantitative Data
=+c) Discuss what the display reveals about the variable and its distribution.
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