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Introductory Business Statistics

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Introductory Business StatisticsSolutions
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Table of contents
  1. Preface
  2. 1 Sampling and Data
    1. Introduction
    2. 1.1 Definitions of Statistics, Probability, and Key Terms
    3. 1.2 Data, Sampling, and Variation in Data and Sampling
    4. 1.3 Levels of Measurement
    5. 1.4 Experimental Design and Ethics
    6. Key Terms
    7. Chapter Review
    8. Homework
    9. References
    10. Solutions
  3. 2 Descriptive Statistics
    1. Introduction
    2. 2.1 Display Data
    3. 2.2 Measures of the Location of the Data
    4. 2.3 Measures of the Center of the Data
    5. 2.4 Sigma Notation and Calculating the Arithmetic Mean
    6. 2.5 Geometric Mean
    7. 2.6 Skewness and the Mean, Median, and Mode
    8. 2.7 Measures of the Spread of the Data
    9. Key Terms
    10. Chapter Review
    11. Formula Review
    12. Practice
    13. Homework
    14. Bringing It Together: Homework
    15. References
    16. Solutions
  4. 3 Probability Topics
    1. Introduction
    2. 3.1 Terminology
    3. 3.2 Independent and Mutually Exclusive Events
    4. 3.3 Two Basic Rules of Probability
    5. 3.4 Contingency Tables and Probability Trees
    6. 3.5 Venn Diagrams
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Bringing It Together: Practice
    12. Homework
    13. Bringing It Together: Homework
    14. References
    15. Solutions
  5. 4 Discrete Random Variables
    1. Introduction
    2. 4.1 Hypergeometric Distribution
    3. 4.2 Binomial Distribution
    4. 4.3 Geometric Distribution
    5. 4.4 Poisson Distribution
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  6. 5 Continuous Random Variables
    1. Introduction
    2. 5.1 Properties of Continuous Probability Density Functions
    3. 5.2 The Uniform Distribution
    4. 5.3 The Exponential Distribution
    5. Key Terms
    6. Chapter Review
    7. Formula Review
    8. Practice
    9. Homework
    10. References
    11. Solutions
  7. 6 The Normal Distribution
    1. Introduction
    2. 6.1 The Standard Normal Distribution
    3. 6.2 Using the Normal Distribution
    4. 6.3 Estimating the Binomial with the Normal Distribution
    5. Key Terms
    6. Chapter Review
    7. Formula Review
    8. Practice
    9. Homework
    10. References
    11. Solutions
  8. 7 The Central Limit Theorem
    1. Introduction
    2. 7.1 The Central Limit Theorem for Sample Means
    3. 7.2 Using the Central Limit Theorem
    4. 7.3 The Central Limit Theorem for Proportions
    5. 7.4 Finite Population Correction Factor
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  9. 8 Confidence Intervals
    1. Introduction
    2. 8.1 A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size
    3. 8.2 A Confidence Interval for a Population Standard Deviation Unknown, Small Sample Case
    4. 8.3 A Confidence Interval for A Population Proportion
    5. 8.4 Calculating the Sample Size n: Continuous and Binary Random Variables
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  10. 9 Hypothesis Testing with One Sample
    1. Introduction
    2. 9.1 Null and Alternative Hypotheses
    3. 9.2 Outcomes and the Type I and Type II Errors
    4. 9.3 Distribution Needed for Hypothesis Testing
    5. 9.4 Full Hypothesis Test Examples
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  11. 10 Hypothesis Testing with Two Samples
    1. Introduction
    2. 10.1 Comparing Two Independent Population Means
    3. 10.2 Cohen's Standards for Small, Medium, and Large Effect Sizes
    4. 10.3 Test for Differences in Means: Assuming Equal Population Variances
    5. 10.4 Comparing Two Independent Population Proportions
    6. 10.5 Two Population Means with Known Standard Deviations
    7. 10.6 Matched or Paired Samples
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. Bringing It Together: Homework
    14. References
    15. Solutions
  12. 11 The Chi-Square Distribution
    1. Introduction
    2. 11.1 Facts About the Chi-Square Distribution
    3. 11.2 Test of a Single Variance
    4. 11.3 Goodness-of-Fit Test
    5. 11.4 Test of Independence
    6. 11.5 Test for Homogeneity
    7. 11.6 Comparison of the Chi-Square Tests
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. Bringing It Together: Homework
    14. References
    15. Solutions
  13. 12 F Distribution and One-Way ANOVA
    1. Introduction
    2. 12.1 Test of Two Variances
    3. 12.2 One-Way ANOVA
    4. 12.3 The F Distribution and the F-Ratio
    5. 12.4 Facts About the F Distribution
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  14. 13 Linear Regression and Correlation
    1. Introduction
    2. 13.1 The Correlation Coefficient r
    3. 13.2 Testing the Significance of the Correlation Coefficient
    4. 13.3 Linear Equations
    5. 13.4 The Regression Equation
    6. 13.5 Interpretation of Regression Coefficients: Elasticity and Logarithmic Transformation
    7. 13.6 Predicting with a Regression Equation
    8. 13.7 How to Use Microsoft Excel® for Regression Analysis
    9. Key Terms
    10. Chapter Review
    11. Practice
    12. Solutions
  15. A | Statistical Tables
  16. B | Mathematical Phrases, Symbols, and Formulas
  17. Index
1.
xP(x)
00.12
10.18
20.30
30.15
40.10
50.10
60.05
Table 4.6
3.

0.10 + 0.05 = 0.15

5.

1

7.

0.35 + 0.40 + 0.10 = 0.85

9.

1(0.15) + 2(0.35) + 3(0.40) + 4(0.10) = 0.15 + 0.70 + 1.20 + 0.40 = 2.45

11.
xP(x)
00.03
10.04
20.08
30.85
Table 4.7
13.

Let X = the number of events Javier volunteers for each month.

15.
x P(x)
00.05
10.05
20.10
30.20
40.25
50.35
Table 4.8
17.

1 – 0.05 = 0.95

18.

X = the number of business majors in the sample.

19.

2, 3, 4, 5, 6, 7, 8, 9

20.

X = the number that reply “yes”

22.

0, 1, 2, 3, 4, 5, 6, 7, 8

24.

5.7

26.

0.4151

28.

X = the number of freshmen selected from the study until one replied "yes" that same-sex couples should have the right to legal marital status.

30.

1,2,…

32.

1.4

35.

0, 1, 2, 3, 4, …

37.

0.0485

39.

0.0214

41.

X = the number of U.S. teens who die from motor vehicle injuries per day.

43.

0, 1, 2, 3, 4, ...

45.

No

48.
  1. X = the number of pages that advertise footwear
  2. 0, 1, 2, 3, ..., 20
  3. 3.03
  4. 1.5197
50.
  1. X = the number of Patriots picked
  2. 0, 1, 2, 3, 4
  3. Without replacement
53.

X = the number of patients calling in claiming to have the flu, who actually have the flu.

X = 0, 1, 2, ...25

55.

0.0165

57.
  1. X = the number of DVDs a Video to Go customer rents
  2. 0.12
  3. 0.11
  4. 0.77
59.

d. 4.43

61.

c

63.
  • X = number of questions answered correctly
  • X ~ B ( 32,  1 3 ) ( 32,  1 3 )
  • We are interested in MORE THAN 75% of 32 questions correct. 75% of 32 is 24. We want to find P(x > 24). The event "more than 24" is the complement of "less than or equal to 24."
  • P(x > 24) = 0
  • The probability of getting more than 75% of the 32 questions correct when randomly guessing is very small and practically zero.
65.
  1. X = the number of college and universities that offer online offerings.
  2. 0, 1, 2, …, 13
  3. X ~ B(13, 0.96)
  4. 12.48
  5. 0.0135
  6. P(x = 12) = 0.3186 P(x = 13) = 0.5882 More likely to get 13.
67.
  1. X = the number of fencers who do not use the foil as their main weapon
  2. 0, 1, 2, 3,... 25
  3. X ~ B(25,0.40)
  4. 10
  5. 0.0442
  6. The probability that all 25 not use the foil is almost zero. Therefore, it would be very surprising.
69.
  1. X = the number of audits in a 20-year period
  2. 0, 1, 2, …, 20
  3. X ~ B(20, 0.02)
  4. 0.4
  5. 0.6676
  6. 0.0071
71.
  1. X = the number of matches
  2. 0, 1, 2, 3
  3. In dollars: −1, 1, 2, 3
  4. 1 2 1 2
  5. The answer is −0.0787. You lose about eight cents, on average, per game.
  6. The house has the advantage.
73.
  1. X ~ B(15, 0.281)
    This histogram shows a binomial probability distribution. It is made up of bars that are fairly normally distributed. The x-axis shows values from 0 to 15, with bars from 0 to 9. The y-axis shows values from 0 to 0.25 in increments of 0.05.
    Figure 4.4
    1. Mean = μ = np = 15(0.281) = 4.215
    2. Standard Deviation = σ = npq npq = 15(0.281)(0.719) 15(0.281)(0.719) = 1.7409
  3. P(x > 5)=1 – 0.7754 = 0.2246
    P(x = 3) = 0.1927
    P(x = 4) = 0.2259
    It is more likely that four people are literate that three people are.
75.
  1. X = the number of adults in America who are surveyed until one says he or she will watch the Super Bowl.
  2. X ~ G(0.40)
  3. 2.5
  4. 0.0187
  5. 0.2304
77.


  1. X = the number of pages that advertise footwear
  2. X takes on the values 0, 1, 2, ..., 20
  3. X ~ B(20, 2919229192)
  4. 3.02
  5. No
  6. 0.9997
  7. X = the number of pages we must survey until we find one that advertises footwear. X ~ G(2919229192)
  8. 0.3881
  9. 6.6207 pages
79.

0, 1, 2, and 3

81.
  1. X ~ G(0.25)
    1. Mean = μ = 1 p 1 p = 1 0.25 1 0.25 = 4
    2. Standard Deviation = σ = 1−p p 2 1−p p 2 = 1−0.25 0.25 2 1−0.25 0.25 2 ≈ 3.4641
  3. P(x = 10) = 0.0188
  4. P(x = 20) = 0.0011
  5. P(x ≤ 5) = 0.7627
82.
  1. X ~ P(5.5); μ = 5.5; σ =  5.5 σ =  5.5 ≈ 2.3452
  2. P(x ≤ 6) ≈ 0.6860
  3. There is a 15.7% probability that the law staff will receive more calls than they can handle.
  4. P(x > 8) = 1 – P(x ≤ 8) ≈ 1 – 0.8944 = 0.1056
84.

Let X = the number of defective bulbs in a string.

Using the Poisson distribution:

  • μ = np = 100(0.03) = 3
  • X ~ P(3)
  • P(x ≤ 4) ≈ 0.8153

Using the binomial distribution:

  • X ~ B(100, 0.03)
  • P(x ≤ 4) = 0.8179

The Poisson approximation is very good—the difference between the probabilities is only 0.0026.

86.
  1. X = the number of children for a Spanish woman
  2. 0, 1, 2, 3,...
  3. 0.2299
  4. 0.5679
  5. 0.4321
88.
  1. X = the number of fortune cookies that have an extra fortune
  2. 0, 1, 2, 3,... 144
  3. 4.32
  4. 0.0124 or 0.0133
  5. 0.6300 or 0.6264
  6. As n gets larger, the probabilities get closer together.
90.
  1. X = the number of people audited in one year
  2. 0, 1, 2, ..., 100
  3. 2
  4. 0.1353
  5. 0.3233
92.
  1. X = the number of shell pieces in one cake
  2. 0, 1, 2, 3,...
  3. 1.5
  4. 0.2231
  5. 0.0001
  6. Yes
94.

d

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