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Solution Manual for Business Statistics, 3rd Edition

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    S OLUTIONS M ANUAL D IRK T EMPELAAR Masstricht University B USINESS S TATISTICS T HIRD E DITION Robert A. Donnelly

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    Table of Contents Chapter 1: An Introduction to Business Statistics………………………………………………1-1 Chapter 2: Displaying Descriptive Statistics……………………………………………………2-1 Chapter 3: Calculating Descriptive Statistics………………………………………...…………3-1 Chapter 4: Introduction to Probabilities…………………………………………...……………4-1 Chapter 5: Discrete Probability Distributions…………………………………………..………5-1 Chapter 6: Continuous Probability Distributions……………………………………………….6-1 Chapter 7: Sampling and Sampling Distributions………………………………………………7-1 Chapter 8: Confidence Intervals………………………………………………………………...8-1 Chapter 9: Hypothesis Testing for a Single Population………………………………………...9-1 Chapter 10: Hypothesis Tests Comparing Two Populations…………………………………..10-1 Chapter 11: Analysis of Variance (ANOVA) Procedures……………………………………..11-1 Chapter 12: Chi-Square Tests………………………………………………………………….12-1 Chapter 13: Hypothesis Tests for the Population Variance……………………………………13-1 Chapter 14: Correlation and Simple Linear Regression……………………………………….14-1 Chapter 15: Multiple Regression and Model Building………………………………………...15-1 Chapter 16: Forecasting………………………………………………………………………..16-1 Chapter 17: Decision Analysis………………………………………………………………...17-1 Chapter 18: Nonparametric Statistics………………………………………………………….18-1

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    1-1 CHAPTER 1 An Introduction to Business Statistics 1.1 Quantitative/Interval. The differences between average monthly temperatures are meaningful, but there is no true zero point, i.e., absence of temperature. 1.2 Quantitative/Ratio. The differences between average monthly rainfalls are meaningful, and there is a true zero point, because there may be a month without any rainfalls. 1.3 Qualitative/Ordinal. You can rank education level, but the differences between different educational levels cannot be measured. 1.4 Qualitative/Nominal. The marital status is just a label without a meaningful difference, or ranking. 1.5 Quantitative/Ratio. The differences between ages of respondents are meaningful and there is a true zero point: an age of the respondents that equals zero represents the absence of age. 1.6 Qualitative/Nominal. The genders are merely labels with no ranking or meaningful difference. 1.7 Quantitative/Interval. The differences between birth years are meaningful, but there is no true zero point with calendar years. 1.8 Qualitative/ Nominal. The political affiliations are merely labels with no ranking or meaningful difference. 1.9 Qualitative/ Nominal. The races of the respondents are merely labels with no ranking or meaningful difference. 1.10 Qualitative/ Ordinal. You can rank the performance rating, but the differences between different performance ratings cannot be measured. 1.11 Qualitative/ Nominal. The uniform numbers of each member of the school’s sport team are labels with no ranking or meaningful difference. 1.12 Qualitative/ordinal. The differences in the data values between class ranks are not meaningful.

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    1-2 Chapter 1 1.13 Quantitative/Ratio. The differences between final exam scores for your statistics class are meaningful, and there is a true zero point because a student who did not take the exam would have a score of zero. 1.14 Qualitative/Nominal. The state in which the respondents in a survey reside is a label and it is meaningless to talk about the rating of this value. 1.15 Quantitative/Interval. The differences between SAT scores for graduating high school students are meaningful, but there is no true zero point because a student with an SAT score equal to zero does not indicate the absence of a score. 1.16 Qualitative/Ordinal. You can rank movie ratings, but the differences between different ratings cannot be measured. 1.17 Qualitative/ordinal. The differences in the data values between ratings are not meaningful. 1.18 Qualitative/ordinal. The differences in the data values between ratings are not meaningful. 1.19 Cross-sectional 1.20 Time series 1.21 Time series: Men weekly earnings over the five years. Time series: Women weekly earnings over the five years. 1.22 Cross-sectional data: Men and women workers weekly earnings for any one particular year. 1.23 Cross-sectional: The number of 8x10, 11x14 and 13x19 prints sold over a particular year. 1.24 Time series: the number of 8x10 prints sold over the four years. Time series: the number of 11x14 prints sold over the four years. Time series: the number of 13x19 prints sold over the four years. 1.25 Descriptive statistics, because it identifies a sample mean. 1.26 Inferential statistics, because the statements about comparing the average costs of a hotel room in two states was based on results from samples taken from two populations.

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    An Introduction to Business Statistics 1-3 1.27 Inferential statistics, because it would not be feasible to get the credit card debt from every graduate student in the country. These results would be based on a sample of the population used to make an inference about the entire population. 1.28 Descriptive statistics, because we summarize reviewer scores without going into inference. 1.29 Inferential statistics, because it would not be feasible to survey every American in the country. These results are based on a sample of the population used to make an inference on the entire population. 1.30 Descriptive statistics, because this percentage represents the proportion of a specific group of customers arriving before 6 PM and is not making an inference about the entire population of customers.

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    2-1 CHAPTER 2 Displaying Descriptive Statistics 2.1 a) 7 2 128 100   therefore use 7 classes. b) 9 2 512 300   therefore use 9 classes. c) 10 2 1,024 1,000   therefore use 10 classes. d) 11 2 2,048 2,000   therefore use 11 classes. 2.2 6 2 64 50   therefore use 6 classes. 74 16 Estimated Class Width 9.7 10 6     a) 16-25, 26-35, 36-45, 46-55, 56-65, 66-75 b) 16 to under 26, 26 to under 36, 36 to under 46, 46 to under 56, 56 to under 66, 66 to under 76 2.3 Cumulative Frequency Relative Relative Number Frequency Frequency 1 6 0.250 0.250 2 6 0.250 0.500 3 5 0.208 0.708 4 4 0.167 0.875 5 3 0.125 1.00 Total 24 1.00 2.4 5 2 32 30   therefore use 5 classes. 42.8 13.9 Estimated Class Width 5.8 6 5    

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    2-2 Chapter 2 Cumulative Frequency Relative Relative Class Frequency Frequency 13 to less than 19 6 0.200 0.200 19 to less than 25 11 0.367 0.567 25 to less than 31 4 0.133 0.700 31 to less than 37 7 0.233 0.933 37 to less than 43 2 0.067 1.0 Total 30 1.00 2.5 6 2 64 36   therefore use 6 classes. $5,927 $162 Estimated Class Width $960 $1, 000 6     a, b, c) Cumulative Frequency Relative Relative Class Frequency Frequency Less than $1,000 12 0.333 0.333 $1,000 to less than $2,000 8 0.222 0.555 $2,000 to less than $3,000 3 0.083 0.638 $3,000 to less than $4,000 2 0.056 0.694 $4,000 to less than $5,000 6 0.167 0.861 $5,000 to less than $6,000 5 0.139 1.000 Total 36 1.000 d) The following histogram was constructed using bins $999, $1,999, $2,999, $3,999, $4,999, and $5,999.

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    Displaying Descriptive Statistics 2-3 2.6 5 2 32 25   therefore use 5 classes. 46 18 Estimated Class Width 5.6 6 5     a, b, c) Cumulative Frequency Relative Relative Class Frequency Frequency 18-23 2 0.08 0.08 24-29 6 0.24 0.32 30-35 5 0.20 0.52 36-41 5 0.20 0.72 42-47 7 0.28 1.00 Total 25 1.00 d) The following histogram was constructed using bins 23, 29, 35, 41, and 47.

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    2-4 Chapter 2 2.7 a, b, c) Cumulative Frequency Relative Relative Number Frequency Frequency 0 3 0.043 0.043 1 21 0.300 0.343 2 23 0.329 0.672 3 15 0.214 0.886 4 8 0.114 1.000 Total 70 1.000 d) The following histogram was constructed using bins 0, 1, 2, 3, and 4. 2.8 6 2 64 40   therefore use 6 classes. 76 19 Estimated Class Width (Current) 9.5 10 6     Results would be similar using the laid-off ages. Class Bins Midpoint 19 to less than 29 28.9 24 29 to less than 39 38.9 34 39 to less than 49 48.9 44 49 to less than 59 58.9 54 59 to less than 69 68.9 64 69 to less than 79 78.9 74

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    Displaying Descriptive Statistics 2-5 An extra bin (18.9) was added to Excel to provide the open-ended class required by PHStat. a) b) According to these ogives, it appears that the current workforce is younger than the laid-off employees. It appears that the laid-off employees may have a case for age discrimination. 2.9 9 2 512 350   therefore use 9 classes. $349.99 $2.19 Estimated Class Width $38.64 $40 9     a, b, c) Cumulative Frequency Relative Relative Class Frequency Frequency Less than $40 52 0.149 0.149 $40 to less than $80 103 0.294 0.443 $80 to less than $120 91 0.260 0.703 $120 to less than $160 65 0.186 0.889 $160 to less than $200 15 0.043 0.932 $200 to less than $240 11 0.031 0.963 $240 to less than $280 5 0.014 0.977 $280 to less than $320 5 0.014 0.991 $320 to less than $360 3 0.009 1.000 Total 350 1.000

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    2-6 Chapter 2 d) The following histogram was constructed using bins 39.999, 79.999, 119.999, 159.999, 199.999, 239.999, 279.999, 319.999, and 359.999. 2.10 7 2 128 125   therefore use 7 classes. 83.2 71.0 Estimated Class Width 1.7 2 7     a, b, c) Cumulative Frequency Relative Relative Class Frequency Frequency 71 to less than 73 5 0.040 0.040 73 to less than 75 37 0.296 0.336 75 to less than 77 44 0.352 0.688 77 to less than 79 31 0.248 0.936 79 to less than 81 6 0.048 0.984 81 to less than 83 1 0.008 0.992 83 to less than 85 1 0.008 1.000 Total 125 1.000 d) The following histogram was constructed using bins 72.99, 74.99, 76.99, 78.99, 80.99, 82.99, and 84.99.

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    Displaying Descriptive Statistics 2-7 e) For 68.8% of the days, ocean temps were lower than 77 degrees. 2.11 a, b, c) Cumulative Frequency Relative Relative Category Frequency Frequency Google 20 0.667 0.667 Yahoo 5 0.167 0.833 Bing 2 0.067 0.900 Baidu 2 0.067 0.967 Other 1 0.033 1.000 Total 30 1.000

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    2-8 Chapter 2 d) 2.12 a, b, c) Cumulative Frequency Relative Relative Category Frequency Frequency Excellent 16 0.267 0.267 Good 31 0.517 0.783 Fair 8 0.133 0.917 Poor 5 0.083 1.000 Total 60 1.000 d) e) 78.3% rated their dining experience as either Excellent or Good.

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    Displaying Descriptive Statistics 2-9 2.13 2.14

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    2-10 Chapter 2 2.15 2.16

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