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Business Statistics in Practice: Using Data, Modeling, and Analytics, 8th Edition Solution Manual

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    Chapter 01 - An Introduction to Business Statistics 1 - 1 CHAPTER 1 — An Introduction to Business Statistics 1. 1 Any characteristic of a population unit is called a variable. Quantitative: values on the real number line. Qualitative: record unit into categories. L 01 - 0 1, L 01 - 0 2 1.2 a. Quantitative; dollar amounts correspond to values on the real number line. b. Quantitative; net profit is a dollar amount. c. Qualitative; which stock exchange is a category. d. Quantitative; national debt is a dollar amount. e. Qualitative; media is categorized into radio, television, or print. L01 - 0 2 1. 3 Cross sectional data are collected at approximately the same point in time whereas time series data are collected over different time periods. The total number of cars sold in 2009 by 10 different sales people are cross sectional data. The total number of cars sold by a particular sales person for the years 2005 – 2009 are time series data. L01 - 03 1.4 The response variable is whether or not the person has cancer. The factors or independent variables are age, sex, occupation, and number of cigarettes smoked per day. This is an observational study. L01 - 05 1.5 $398,000 L01 - 0 1 1.6 Diamond: Lake Lot $494,000 Rudy: Lake Lot $447,000 L01 - 0 1

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    Chapter 01 - An Introduction to Business Statistics 1 - 2 1.7 This chart shows sales are increasing over time. L 01 - 0 4 1.8 A population is a set of existing units. Consumers utilizing a particular product. L01 - 0 6 1. 9 Census: examine all of the population units. Sample: subset of the units in a population. L01 - 0 6 1. 10 Descriptive statistics: science of describing the important aspects of a set of measurements. Statistical inference: science of using a sample of measurements to make generalizations about the important aspects of a population of measurements. L01 - 0 7 1.11 A process is a series of operations that take input(s) and generate output(s). L01 - 0 6 1.12 Most of the scores would fall between 36 and 48 because 36 is the smallest score in the sample and 48 is the largest score in the sample. An estimate of the proportion of scores that would be at least 42 is 46/65 = 0.708 because 46 of the 65 sample scores are at least 42. L01 - 0 8 1.1 3 Most waiting times will be from 0 .4 to 11.6 minutes. An estimate of the proportion of waiting times less than 6 minutes is found by counting the number of customers with waiting times 0 100 200 300 400 500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Sales Bismark X - 12 Calculator Monthly Sales

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    Chapter 01 - An Introduction to Business Statistics 1 - 3 less than 6 minutes and dividing by the total of 100 customers. . 6 . 100 60 = L01 - 0 8 1.14 Most breaking strengths will be between 46.8 lbs and 54 lbs. L01 - 0 8 1. 15 A ratio variable is a quantitative variable measured on a scale such that ratios of values of the variables are meaningful and there is an inherently defined zero value. An interval variable is a quantitative variable such that ratios of values of the variable are not meaningful and there is not an inherently defined zero value. L01 - 0 9 1. 16 An ordinal variable is a qualitative variable such that there is a meaningful ordering, or ranking, of the cat egories. A nominative variable is a qualitative variable such that there is no meaningful ordering, or ranking, of the categories. L01 - 0 9 1. 17 Ordinal, nominative, ordinal, nominative, ordinal, and nominative. L01 - 0 9 1. 18 Nominative, ordinal, ordinal, ordinal, nominative, and nominative. L01 - 0 9 1.19 130 135 140 145 150 155 160 165 170 175 180 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 Coffee Temperature in Degrees F

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    Chapter 01 - An Introduction to Business Statistics 1 - 4 Basing the limits on the minimum and maximum temperatures observed, the lower limit is 146 de grees and the upper limit is 173 degrees. L01 - 04, L01 - 0 8 1.2 0 The process is not in statistical control and the higher percentages of people waiting too long occur early in the we ek. A potential solution is to staff at a higher level early in the week. L01 - 0 4

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    Chapter 02 - Descriptive Statistics: Tabular and Graphical Methods 2 - 1 CHAPTER 2 — Descriptive Statistics: Tabular and Graphical Methods 2.1 Constructing either a frequency or a relative frequency distribution helps identify and quantify patterns in how often various categories occur. L02 - 01 2.2 Relative frequency of any category is calculated by counting the number of occurrences of the category divided by the total number of observations. Percent frequency is calculated by multiplying relative frequency by 100. L02 - 01 2.3 Answers and examples will vary. L02 - 01 2.4 a. Relative Percent Category / Class Frequency Frequency Frequency A 100 0.40 40% B 25 0.10 10% C 75 0.30 30% D 50 0.20 20% b. Bar Chart of Grade Frequency 0 20 40 60 80 100 120 A B C D Answer Frequency L02 - 01 2.5 a. (100 / 250) * 360 degrees = 144 degrees b. (25 / 250) * 360 degrees = 36 degrees c. Pie Chart of Grade Frequency 40% 10% 30% 20% A B C D

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    Chapter 02 - Descriptive Statistics: Tabular and Graphical Methods 2 - 2 L02 - 01 2.6 a. Relative frequency for product x is 1 – (0.15 + 0.36 + 0.28) = 0.21 b. Product: W X Y Z 75 105 180 140 c. Percent Frequency Bar Chart For Product 0% 5% 10% 15% 20% 25% 30% 35% 40% W X Y Z Product Percent Frequency d. Degrees for W would be 54, for X degrees would be 75.6, for Y 129.6, and for Z 100.8. L02 - 01 2.7 a. Rating Frequency Relative Frequency Outstanding 14 0.467 Very Good 10 0.333 Good 5 0.167 Average 1 0.033 Poor 0 0.000 b.

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    Chapter 02 - Descriptive Statistics: Tabular and Graphical Methods 2 - 3 c. L02 - 01 2.8 a. Tally for Discrete Variables: Sports League Sports Rel. League Count Freq. Percent MLB 11 0.22 22.00 MLS 3 0.06 6.00 NBA 8 0.16 16.00 NFL 23 0.46 46.00 NHL 5 0.10 10.00 N= 50 b. Sports League Count NHL NFL NBA MLS MLB 25 20 15 10 5 0 Chart of Sports League

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    Chapter 02 - Descriptive Statistics: Tabular and Graphical Methods 2 - 4 c. MLB MLS NBA NFL NHL Category 5 23 8 3 11 Pie Chart of Sports League d. Most popular league is NFL and least popular is MLS. L02 - 01 2.9 US Market Share In 2005 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% Daimler- Chrysler Ford GM Japanese Other Imports Manufacturer Percent Chrysler Dodge Jeep

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    Chapter 02 - Descriptive Statistics: Tabular and Graphical Methods 2 - 5 US Market Shares In 2005 14% 18% 26% 28% 14% Daimler-Chrysler Ford GM Japanese Other Imports L02 - 01 2.10 Comparing the two pie charts they show that since 2005 Ford & GM, have lost market share, while Chrysler and Japanese models have increased market share. L02 - 01 2.11 Medical Ins. Coverage For Income < $30,000 per year Medicare/Medic aid, 33% Private, 50% None, 17% Medical Ins. Coverage For Income > $75,000 per year Medicare/Medic aid, 9% Private, 87% None, 4% C hrysler Dodge Jeep

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    Chapter 02 - Descriptive Statistics: Tabular and Graphical Methods 2 - 6 L02 - 01 2.12 a. 32.29% b. 4.17% c. Explanations will vary L02 - 02 2.13 a. We construct a frequency distribution and a histogram for a data set so we can gain some insight into the shape, center, and spread of the data along with whether or not outliers exist. b. A frequency histogram represents the frequency in a class using bars while in a frequency polygon the frequencies in consecutive classes are connected by a line. c. A frequency ogive represents a cumulative distribution while the frequency polygon is not a cumulative distribution. Also, in a frequency polygon the lines connect the class midpoints while in a frequency ogive the lines connect the upper boundaries of the classes. L02 - 03 2.14 a. To find the frequency for a class you simply count how many of the observations are greater than or equal to the lower boundary and less than the upper boundary. b. Once you get the frequency for a class the relative frequency is obtained by dividing the class frequency by the total number of observations (data points). c. Percent frequency for a class is calculated by multiplying the relative frequency by 100. L02 - 03 2.15 a. One hump in the middle; left side looks like right side. b. Two humps, left side may or may not look like right side.

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    Chapter 02 - Descriptive Statistics: Tabular and Graphical Methods 2 - 7 c. Long tail to the right d. Long tail to the left L02 - 03 2.16 a. Since there are 28 points you should use 5 classes (from Table 2.5). b. Class Length (CL) = (46 – 17) / 5 = 6 c. 17 ≤ x < 23, 23 ≤ x < 29, 29 ≤ x < 35, 35 ≤ x < 41, 41 ≤ x < 47 d. Frequency Distribution - Quantitative Data cumulative lower upper midpoint width frequency percent frequency percent 12 < 18 15 6 1 3.6 1 3.6 18 < 24 21 6 3 10.7 4 14.3 24 < 30 27 6 2 7.1 6 21.4 30 < 36 33 6 5 17.9 11 39.3 36 < 42 39 6 14 50.0 25 89.3 42 < 48 45 6 3 10.7 28 100.0 28 100.0

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    Chapter 02 - Descriptive Statistics: Tabular and Graphical Methods 2 - 8 e. f. See output in answer to d. L02 - 03 2.17 a & b. c. Cum Percent Cum % Class Frequency Frequency Frequency Frequency 50 < 60 2 2 4% 4% 60 < 70 5 7 10% 14% 70 < 80 14 21 28% 42% 80 < 90 17 38 34% 76% 90 < 100 12 50 24% 100% Total 50 50 100%

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    Chapter 02 - Descriptive Statistics: Tabular and Graphical Methods 2 - 9 Frequency Polygon 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 40 50 60 70 80 90 Data Percent d. Ogive 0.0 25.0 50.0 75.0 100.0 40 50 60 70 80 90 Data Cumulative Percent L02 - 03 2.18 a. 6 classes because there are 60 data points (from Table 2.5). b. Class Length (CL) = (35 – 20) / 6 = 2.5 and we round up to 3. c. 20 ≤ x < 23, 23 ≤ x < 26, 26 ≤ x < 29, 29 ≤ x < 32, 32 ≤ x < 35, 35 ≤ x < 38 d. Rating cumulative lower upper midpoint width frequency Percent frequency percent 20 < 23 21.5 3 2 3.3 2 3.3 23 < 26 24.5 3 3 5.0 5 8.3

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    Chapter 02 - Descriptive Statistics: Tabular and Graphical Methods 2 - 10 26 < 29 27.5 3 9 15.0 14 23.3 29 < 32 30.5 3 19 31.7 33 55.0 32 < 35 33.5 3 26 43.3 59 98.3 35 < 38 36.5 3 1 1.7 60 100.0 60 100.0

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    Chapter 02 - Descriptive Statistics: Tabular and Graphical Methods 2 - 11 e. Histogram 0 5 10 15 20 25 30 20 23 26 29 32 35 Rating Frequency Distribution shape is skewed left. L02 - 03 2.19 a & b. Rating cumulative lower upper midpoint width frequency Percent frequency percent 20 < 23 21.5 3 2 3.3 2 3.3 23 < 26 24.5 3 3 5.0 5 8.3 26 < 29 27.5 3 9 15.0 14 23.3 29 < 32 30.5 3 19 31.7 33 55.0 32 < 35 33.5 3 26 43.3 59 98.3 35 < 38 36 .5 3 1 1.7 60 100.0 60 100.0

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