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Introduction to Business Statistics, 7th Edition Solution Manual

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    1 CHAPTER 1 A PREVIEW OF BUSINESS STATISTICS SECTION EXERCISES 1.1 d/p/e In ancient times, statistics was mainly employed for counting people or possessions in order to facilitate taxation. 1.2 d/p/m Statistical methods are useful in all facets of business today. Statistics can be used to describe information, to analyze data, to reach conclusions, and to make decisions. 1.3 d/p/m Descriptive statistics are used to summarize and describe a set of data. Inferential statistics are used to make generalizations, estimates, forecasts, or other judgments about the population from which the data (sample) is taken. Inferential statistics are involved when a state senator surveys some of her constituents in order to obtain guidance on how she should vote. She is using statistics to make judgments about the population based on the data from the sample . 1.4 d/p/m This represents descriptive statistics; we are summarizing and describing the data. 1.5 d/p/m This information represents inferential statistics since we are using information collected from a sample of 20 adults to make inferences about all adults. 1.6 d/p/e Qualitative variables or "attributes" involve counting the number of people or objects that fall within categories. Quantitative variables determine how much of something is possessed. 1.7 d/p/e Discrete quantitative variables can take on only certain values along an interval, with the values having gaps between them. Discrete variables are applicable when we want to count the num ber of times something occurs. Continuous quantitative variables can take on any value along an interval. Continuous vari ables are applicable when there are no gaps between the exact values which these variables can take on, such as weight, height, volume, or distance. Note: In this solutions manual, exercises are categorized according to type, tools required, and level of difficulty: Type: Tools: Difficulty: d = definitional/conceptual p = pencil e = easy c = computational a = calculator m = moderate p = problem c = computer d = difficult For example, "c/a/m" refers to an exercise that is computational in nature, requires a pocket calculator, and is judged to be moderate in difficulty. The classifications are of necessity subjective. We have attempted to specify the most basic tool that could be practical for the task. In some cases (e.g., simple regression), the pocket calculator can be used even though a computer statistical package (if available) is preferred. In other cases (e.g., multiple regression and analysis of variance), the computer is automatically specified as the required tool. 1.8 d/p/m

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    2 a. This information might be interpreted as a qualitative variable if we view it as expressing that the school is among those which have been accredited for the past 15 years versus those which have not been accredited for the past 15 years. b. This information might be interpreted as a quantitative variable if we view it as counting the number of years the school has been accredited during the past 15 - year period. For other locksmithing schools over the past 15 years, the number of years they have been accredited could be any integer value from 0 to 15. 1.9 d/p/m a. This information is on the ordinal scale. The industries are viewed in terms of rank instead of the distance between them. However, we do not have a unit of measurement to describe how many more strikes Industry A has than Industry B. b. This information is on the ratio scale. The industries can be viewed in terms of rank (C has lost fewer days per worker) , and there is a unit of measurement enabling us to describe how many more days Industry D has lost per worker. Also, t here is an absolute zero point and multiples are meaningful. 1.10 d/p/m a. The lodge might give each guest a number to identify the state in which he or she resides. b. The lodge could rank the rooms at the lodge from most attractive to least attractive. c. The lodge could describe different months of the year according to their average temperatures. d. The lodge could record the number of skiers at the lodge from each one of the New England states. 1.11 d/p/m The restaurant might be able to make decisions pertaining to such matters as the quality of food, the courtesy and number of employees, and the cleanliness of the restaurant. 1.12 d/p/m The company might report the percentage of burglaries in homes with their product versus the percentage in homes without their product . Hopefully, the former percentage is lower than the latter . 1.13 d/p/m The company may manipulate the data to show what it wants to show; for example, by distorting the scale on a graph to make a large deficit appear very small. Another possibility is to use a sample that is not representative of the population. 1.14 d/p/e You should ask yourself what benefits the person or company stands to gain from the conclusions reached by the study. CHAPTER EXERCISES 1.15 d/p/m This information would represent inferential statistics, since a sample is used to make generalizations about the population. 1.16 d/p/m a. Qualitative; you are in one category or the other. b. Qualitative; you are in one category or the other. c. Quantitative, discrete; the number of people that attended is countable (0, 1, 2, … ). d. Quantitative, discrete; the price can take on only certain values along an interval. e. Quantitative, continuous; time can take on a value at any point along an interval. f. Quantitative, discrete; the number of students that belong to a fraternity or sorority is countable. 1.17 d/p/m The amount of money paid out in premiums and the number of policies purchased in the previous year would play a role in how much you pay for your policy. Data such as the number of

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    3 accidents, speeding tickets, or other moving violations you've had in the past few years could also play a role , as could data regarding accident or claim frequencies associated with the type of vehicle you drive. 1.18 d/p/m a. Ratio scale; there is an absolute zero point associated with the number of employees. b. Interval scale; there is no absolute zero point for temperature. c. Nominal scale; we could use "1" to identify yes and "0" for no. d. Ordinal scale; the cars are ranked but there is no measure for the distance between them. 1.19 d/p/m It will help them be come more intelligent consumers of statistical claims and findings. Whether as citizens or as business professionals, such i ndividuals will be better able to protect themselves from those in business or the media who may be either incompetent or unethical. 1.20 d/p/m a. Major: nominal. Each major would be assigned a number. b. Class: ordinal – Freshman, Sopho more, Junior, or Senior. c. SAT score: interval. This value gives him a ranking and there is a unit of measurement, but multiples do not make sense. (The minimum total score is 400, not zero.) d. The $30 used to buy a new calculator: ratio. 1.21 d/p/m a. The population would be all 40 students who are enrolled in the English class. The sample would be the 5 students in the class that Roger questioned. b. This is probably not a representative sample, since Roger chose 5 students that always sit in the back. They may all be friends or may have different opinions than those sitting in the front. 1.22 d/p/m a. This information can be viewed as representing the nominal scale of measurement if we view the stocks in terms of returning more versus not returning more than the rate that had been expected. b. This information can be viewed as representing the ratio scale of measurement . For example, a 40% rate for above - expected performance would be twice a 20% rate. There is an absolute zero, a unit of measurement (percentage point), and multiples are meaningful.

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    5 CHAPTER 2 VISUAL DESCRIPTION OF DATA SECTION EXERCISES 2.1 d/p/e A frequency distribution is a table that divides the data values into classes and shows the number of observed values that fall into each class. By summarizing and reporting data into a frequency distribution, the data can be readily understood and interpreted. 2.2 d/p/m Selecting the number of classes is a subjective process. In general, about 5 to 15 classes will be suitable. 2.3 c/p/m a. 45.59 million b. lower limit is 35, upper limit is under 45 c. 10 years d. 40 years 2.4 c/p/m a. 40.78 million b. lower limit is 25, upper limit is under 35 c. 10 years d. 30 years 2.5 c/p/m a. 183.53 thousand b. lower limit is 45, upper limit is under 55 c. 10 years d. 50 years 2.6 c/p/m a. 34.23 thousand b. lower limit is 15, upper limit is under 25 c. 10 years d. 20 years 2.7 d/p/e Mutually exclusive means a given data value can fall into only one class. Exhaustive means that the set of classes includes all possible data values. 2.8 c/p/m The number of states in each category is shown above the corresponding bar. For example, there are 13 states within the $50 billio n – under $100 billion category. 800 700 600 500 400 300 200 100 0 18 16 14 12 10 8 6 4 2 0 Deposits Frequency 1 1 0 0 0 0 1 0 1 1 1 3 7 5 13 16 Histogram of Deposits 2.9 c/p/m The number of employees in each category is shown above the corresponding bar.

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    6 For example, there are 7 data values within the 2 0 – under 22 category. wage Frequency 26 24 22 20 18 16 9 8 7 6 5 4 3 2 1 0 2 8 7 8 5 Histogram of wage 2.10 c/p/m The number of applicants in each category is shown above the corresponding bar. For example, there were 9 applicants within the 7 0 – under 80 category. Score Frequency 110 100 90 80 70 60 50 9 8 7 6 5 4 3 2 1 0 1 5 5 9 4 1 Histogram of Score 2.11 c/p/m The number of seasons in each goal category is shown above the bars. For example, there were 2 seasons during which Mr. Gretzky’s goal total was in the 7 0 – under 80 category.

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    7 Goals Frequency 100 80 60 40 20 0 4 3 2 1 0 1 1 2 1 4 3 2 3 2 1 Histogram of Goals 2.12 c/a/m Annual Sales Percent Cumulative Frequency Under $10,000 59.30 1262 $ 10,000 - under $ 25,000 12.03 1518 $ 25,000 - under $ 50,000 7.42 1676 $ 50,000 - under $ 100,000 6.58 1816 $ 100,000 - under $ 250,000 7.47 1975 $ 250,000 - under $500,000 3.85 2057 $500,000 - under $1,000,000 1.97 2099 $1,000,000 or more 1.36 2128 2.13 c/a/m Driver Age Percent Cumulative Frequency Under 20 5.29 10.72 20 - under 25 8.31 27.56 25 - under 35 20.12 68.34 35 - under 45 22.49 113.93 45 - under 55 18.10 150.63 55 - under 65 11.50 173.95 65 or older 14.19 202.71 2.14 c/a/m Total Deposits, $ Billions Relative Frequency, % Greater - Than or Within, % 0 - under 100 58.0 100.0

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    8 100 - under 200 24.0 42.0 200 - under 300 8.0 1 8 .0 300 - under 400 4.0 10.0 400 - under 500 2. 0 6 .0 500 - under 600 0.0 4.0 600 - under 700 0 .0 4.0 700 – under 800 4.0 4.0 2.15 c/a/m Less - than Ogive for 50 U.S. States: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 A B C D E F G H I Deposits Percent 0 0 50 32 100 58 150 68 200 82 250 88 300 90 350 92 400 94 450 94 500 96 550 96 600 96 650 96 700 96 750 98 800 100 Less-Than Ogive for 50 U.S. States 0 20 40 60 80 100 120 0 200 400 600 800 Deposits, $Billions Percent 2.16 c/p/m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 A B C D E F G H I Goals Percent 0 0 10 5 20 15 30 30 40 40 50 55 60 75 70 80 80 90 90 95 100 100 Less-Than Ogive for Gretzky Goals Scored 0 20 40 60 80 100 0 20 40 60 80 100 Goals Scored % of Seasons 2.17 c/c/m The number of data values in each category is shown above the bar. For example, there are 10 data values in the $30,00 0 – under $40,000 category. There are two portfolio values at the extremes that seem especially low or high compared to the others.

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    9 Portfolio Frequency 80000 60000 40000 20000 20 15 10 5 0 1 7 18 20 19 10 4 1 Histogram of Portfolio 2.18 c/c/m The number of data values in each category is shown above the bar. For example, there was only one data value in the 28 second s – under 30 seconds category, and this seems to be an especially low time compared to the others. 48 44 40 36 32 28 20 15 10 5 0 Seconds Frequency 0 2 7 9 21 20 13 7 0 0 1 0 Histogram of Seconds 2.19 c/c/m The number of data values in each category is shown above the bar. For example, there are 23 data values in the 55 – under 60 e - mails category. The single value s in the 40 – under 45 and 45 – under 50 categories would appear to be especially low compared to the others.

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    10 80 70 60 50 40 25 20 15 10 5 0 emails Frequency 6 8 14 18 20 23 9 1 1 Histogram of emails 2.20 c/p/m 2.21 c/p/m Stem (Tens) | Leaf (Units) Stem (Tens) | Leaf (Units) 1 | 559 1 | 13799 2 | 014567 2 | 24446889 3 | 458 3 | 0023379 4 | 12688 4 | 1123366689 5 | 17 5 | 22334677799 6 | 24479 6 | 0113 7 | 1257 8 | 13 2.22 c/p/m 20 20 22 22 27 28 30 31 31 33 35 39 41 43 44 44 54 57 2.23 c/p/d It is not possible to determine the exact values because there is not enough detail to determine the units digit. One possible set of data is shown below: 613 695 770 899 955 630 702 864 900 962 633 708 866 903 981 652 721 884 909 677 755 897 936 2.24 c/c/m Stem - and - Leaf Display: Portfolio Stem - and - leaf of Portfoli N = 80 Leaf Unit = 1000

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    11 1 1 9 4 2 033 5 2 7 10 3 12234 15 3 66788 25 4 0111222233 34 4 566668899 (9) 5 001133334 37 5 55566777899 26 6 001111222 17 6 677778889 8 7 003334 2 7 6 1 8 0 Portfolio 80000 72000 64000 56000 48000 40000 32000 24000 Dotplot of Portfolio 2.25 c/c/m Stem - and - Leaf Display: Seconds Stem - and - leaf of Seconds N = 80 Leaf Unit = 0.10

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    12 1 29 1 1 30 1 31 1 32 1 33 3 34 79 8 35 45557 12 36 0589 21 37 145677999 29 38 04556689 (12) 39 122344457778 39 40 0112333456789 26 41 00357778 18 42 033359 12 43 135 9 44 22249 4 45 66 2 46 56 45.0 42.5 40.0 37.5 35.0 32.5 30.0 Seconds Dotplot of Seconds 2.26 c/c/m Stem - and - Leaf Display: emails Stem - and - leaf of emails N = 100

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    13 Leaf Unit = 1.0 1 4 1 2 4 9 11 5 002222344 34 5 55555566778888888999999 (20) 6 00111112223334444444 46 6 555566667777777899 28 7 00001111222244 14 7 55666777 6 8 000134 84 78 72 66 60 54 48 42 emails Dotplot of emails 2.27 c/c/m Stem - and - Leaf Display: Appraisal Stem - and - leaf of Appraisa N = 60 Leaf Unit = 10 1 2 1 5 2 2233 12 2 4445555 20 2 66666777 25 2 99999 (8) 3 00000001 27 3 22233333 19 3 444455555 10 3 677 7 3 888999 1 4 1

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    14 Appraisal 420 390 360 330 300 270 240 210 Dotplot of Appraisal 2.28 c/c/m Stem - and - Leaf Display: meters Stem - and - leaf of meters N = 80 Leaf Unit = 1.0 2 7 12 7 7 56789 19 8 001111233444 37 8 555556666777889999 (19) 9 0011111222333333344 24 9 5566666678999 11 10 00112344 3 10 78 1 11 2 meters 108 102 96 90 84 78 72 Dotplot of meters

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    15 2.29 d/p/m A histogram graphically displays class intervals as well as class frequencies. A bar chart displays the frequencies for a set of categories or classes. Histograms are appropriate for quantitative data, while bar charts are better for qualitative data. 2.30 c/a/m Bar Chart of market shares in 200 7 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 A B C D E F G H I 2007 N. America 69.0 Japan 15.5 Germany 7.4 Other 8.1 2007 Market Shares 0 10 20 30 40 50 60 70 80 N. America Japan Germany Other Region of Manufacture Market Share 2.31 c/p/m

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    16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 A B C D E F G H I Year Income 1993 45161 1994 47012 1995 49687 1996 51518 1997 53350 1998 56061 1999 59981 2000 62228 2001 63278 2002 62732 2003 65093 40000 45000 50000 55000 60000 65000 70000 1993 1995 1997 1999 2001 2003 Year Median family income, $ Income 2.32 c/p/m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 A B C D E F G H Year $/share 1998 1.10 1999 1.39 2000 1.46 2001 1.25 2002 0.70 2003 1.15 2004 1.79 2005 2.04 2006 2.83 2007 1.98 2008 3.76 McDonald's Net Income Per Share 0.00 1.00 2.00 3.00 4.00 5.00 1996 1998 2000 2002 2004 2006 2008 2010 Year $/Share 2.33 c/p/m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 A B C D E F G H I J Year income/share dividends/share 1998 1.10 0.18 1999 1.39 0.20 2000 1.46 0.22 2001 1.25 0.23 2002 0.70 0.24 2003 1.15 0.40 2004 1.79 0.55 2005 2.04 0.67 2006 2.83 1.00 2007 1.98 1.50 2008 3.76 1.63 McDonald's Net Income/Share and Dividends/Share 0.00 1.00 2.00 3.00 4.00 5.00 1996 1998 2000 2002 2004 2006 2008 2010 Year $/Share income/share dividends/share 2.34 c/p/m

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