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Introductory Statistics

Solutions

Introductory StatisticsSolutions
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 Frequency, Frequency Tables, and Levels of Measurement
    5. 1.4 Experimental Design and Ethics
    6. 1.5 Data Collection Experiment
    7. 1.6 Sampling Experiment
    8. Key Terms
    9. Chapter Review
    10. Practice
    11. Homework
    12. Bringing It Together: Homework
    13. References
    14. Solutions
  3. 2 Descriptive Statistics
    1. Introduction
    2. 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
    3. 2.2 Histograms, Frequency Polygons, and Time Series Graphs
    4. 2.3 Measures of the Location of the Data
    5. 2.4 Box Plots
    6. 2.5 Measures of the Center of the Data
    7. 2.6 Skewness and the Mean, Median, and Mode
    8. 2.7 Measures of the Spread of the Data
    9. 2.8 Descriptive Statistics
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. Bringing It Together: Homework
    16. References
    17. 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
    6. 3.5 Tree and Venn Diagrams
    7. 3.6 Probability Topics
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Bringing It Together: Practice
    13. Homework
    14. Bringing It Together: Homework
    15. References
    16. Solutions
  5. 4 Discrete Random Variables
    1. Introduction
    2. 4.1 Probability Distribution Function (PDF) for a Discrete Random Variable
    3. 4.2 Mean or Expected Value and Standard Deviation
    4. 4.3 Binomial Distribution
    5. 4.4 Geometric Distribution
    6. 4.5 Hypergeometric Distribution
    7. 4.6 Poisson Distribution
    8. 4.7 Discrete Distribution (Playing Card Experiment)
    9. 4.8 Discrete Distribution (Lucky Dice Experiment)
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. References
    16. Solutions
  6. 5 Continuous Random Variables
    1. Introduction
    2. 5.1 Continuous Probability Functions
    3. 5.2 The Uniform Distribution
    4. 5.3 The Exponential Distribution
    5. 5.4 Continuous Distribution
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. 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 Normal Distribution (Lap Times)
    5. 6.4 Normal Distribution (Pinkie Length)
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  8. 7 The Central Limit Theorem
    1. Introduction
    2. 7.1 The Central Limit Theorem for Sample Means (Averages)
    3. 7.2 The Central Limit Theorem for Sums
    4. 7.3 Using the Central Limit Theorem
    5. 7.4 Central Limit Theorem (Pocket Change)
    6. 7.5 Central Limit Theorem (Cookie Recipes)
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. References
    13. Solutions
  9. 8 Confidence Intervals
    1. Introduction
    2. 8.1 A Single Population Mean using the Normal Distribution
    3. 8.2 A Single Population Mean using the Student t Distribution
    4. 8.3 A Population Proportion
    5. 8.4 Confidence Interval (Home Costs)
    6. 8.5 Confidence Interval (Place of Birth)
    7. 8.6 Confidence Interval (Women's Heights)
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. References
    14. 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 Rare Events, the Sample, Decision and Conclusion
    6. 9.5 Additional Information and Full Hypothesis Test Examples
    7. 9.6 Hypothesis Testing of a Single Mean and Single Proportion
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. References
    14. Solutions
  11. 10 Hypothesis Testing with Two Samples
    1. Introduction
    2. 10.1 Two Population Means with Unknown Standard Deviations
    3. 10.2 Two Population Means with Known Standard Deviations
    4. 10.3 Comparing Two Independent Population Proportions
    5. 10.4 Matched or Paired Samples
    6. 10.5 Hypothesis Testing for Two Means and Two Proportions
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. Bringing It Together: Homework
    13. References
    14. Solutions
  12. 11 The Chi-Square Distribution
    1. Introduction
    2. 11.1 Facts About the Chi-Square Distribution
    3. 11.2 Goodness-of-Fit Test
    4. 11.3 Test of Independence
    5. 11.4 Test for Homogeneity
    6. 11.5 Comparison of the Chi-Square Tests
    7. 11.6 Test of a Single Variance
    8. 11.7 Lab 1: Chi-Square Goodness-of-Fit
    9. 11.8 Lab 2: Chi-Square Test of Independence
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. Bringing It Together: Homework
    16. References
    17. Solutions
  13. 12 Linear Regression and Correlation
    1. Introduction
    2. 12.1 Linear Equations
    3. 12.2 Scatter Plots
    4. 12.3 The Regression Equation
    5. 12.4 Testing the Significance of the Correlation Coefficient
    6. 12.5 Prediction
    7. 12.6 Outliers
    8. 12.7 Regression (Distance from School)
    9. 12.8 Regression (Textbook Cost)
    10. 12.9 Regression (Fuel Efficiency)
    11. Key Terms
    12. Chapter Review
    13. Formula Review
    14. Practice
    15. Homework
    16. Bringing It Together: Homework
    17. References
    18. Solutions
  14. 13 F Distribution and One-Way ANOVA
    1. Introduction
    2. 13.1 One-Way ANOVA
    3. 13.2 The F Distribution and the F-Ratio
    4. 13.3 Facts About the F Distribution
    5. 13.4 Test of Two Variances
    6. 13.5 Lab: One-Way ANOVA
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. References
    13. Solutions
  15. A | Review Exercises (Ch 3-13)
  16. B | Practice Tests (1-4) and Final Exams
  17. C | Data Sets
  18. D | Group and Partner Projects
  19. E | Solution Sheets
  20. F | Mathematical Phrases, Symbols, and Formulas
  21. G | Notes for the TI-83, 83+, 84, 84+ Calculators
  22. H | Tables
  23. Index
1.

ounces of water in a bottle

3.

2

5.

–4

7.

–2

9.

The mean becomes zero.

11.

z = 2

13.

z = 2.78

15.

x = 20

17.

x = 6.5

19.

x = 1

21.

x = 1.97

23.

z = –1.67

25.

z ≈ –0.33

27.

0.67, right

29.

3.14, left

31.

about 68%

33.

about 4%

35.

between –5 and –1

37.

about 50%

39.

about 27%

41.

The lifetime of a Sunshine CD player measured in years.

43.

P(x < 1)

45.

Yes, because they are the same in a continuous distribution: P(x = 1) = 0

47.

1 – P(x < 3) or P(x > 3)

49.

1 – 0.543 = 0.457

51.

0.0013

53.

56.03

55.

0.1186

57.
  1. Check student’s solution.
  2. 3, 0.1979
59.
  1. Check student’s solution.
  2. 0.70, 4.78 years
61.

c

63.
  1. Use the z-score formula. z = –0.5141. The height of 77 inches is 0.5141 standard deviations below the mean. An NBA player whose height is 77 inches is shorter than average.
  2. Use the z-score formula. z = 1.5424. The height 85 inches is 1.5424 standard deviations above the mean. An NBA player whose height is 85 inches is taller than average.
  3. Height = 79 + 3.5(3.89) = 92.615 inches, which is taller than 7 feet, 8 inches. There are very few NBA players this tall so the answer is no, not likely.
65.
  1. iv
  2. Kyle’s blood pressure is equal to 125 + (1.75)(14) = 149.5.
67.

Let X = an SAT math score and Y = an ACT math score.

  1. X = 720 720 – 520 15 720 – 520 15 = 1.74 The exam score of 720 is 1.74 standard deviations above the mean of 520.
  2. z = 1.5
    The math SAT score is 520 + 1.5(115) ≈ 692.5. The exam score of 692.5 is 1.5 standard deviations above the mean of 520.
  3. X – μ σ X – μ σ = 700 – 514 117 700 – 514 117 ≈ 1.59, the z-score for the SAT. Y – μ σ Y – μ σ = 30 – 21 5.3 30 – 21 5.3 ≈ 1.70, the z-scores for the ACT. With respect to the test they took, the person who took the ACT did better (has the higher z-score).
69.

c

71.

d

73.
  1. X ~ N(66, 2.5)
  2. 0.5404
  3. No, the probability that an Asian male is over 72 inches tall is 0.0082
75.
  1. X ~ N(36, 10)
  2. The probability that a person consumes more than 40% of their calories as fat is 0.3446.
  3. Approximately 25% of people consume less than 29.26% of their calories as fat.
77.
  1. X = number of hours that a Chinese four-year-old in a rural area is unsupervised during the day.
  2. X ~ N(3, 1.5)
  3. The probability that the child spends less than one hour a day unsupervised is 0.0918.
  4. The probability that a child spends over ten hours a day unsupervised is less than 0.0001.
  5. 2.21 hours
79.
  1. X = the distribution of the number of days a particular type of criminal trial will take
  2. X ~ N(21, 7)
  3. The probability that a randomly selected trial will last more than 24 days is 0.3336.
  4. 22.77
81.
  1. mean = 5.51, s = 2.15
  2. Check student's solution.
  3. Check student's solution.
  4. Check student's solution.
  5. X ~ N(5.51, 2.15)
  6. 0.6029
  7. The cumulative frequency for less than 6.1 minutes is 0.64.
  8. The answers to part f and part g are not exactly the same, because the normal distribution is only an approximation to the real one.
  9. The answers to part f and part g are close, because a normal distribution is an excellent approximation when the sample size is greater than 30.
  10. The approximation would have been less accurate, because the smaller sample size means that the data does not fit normal curve as well.
83.
  1. mean = 60,136
     s = 10,468
  2. Answers will vary.
  3. Answers will vary.
  4. Answers will vary.
  5. X ~ N(60136, 10468)
  6. 0.7440
  7. The cumulative relative frequency is 43/60 = 0.717.
  8. The answers for part f and part g are not the same, because the normal distribution is only an approximation.
85.
  • n = 100; p = 0.1; q = 0.9
  • μ = np = (100)(0.10) = 10
  • σ = npq npq = (100)(0.1)(0.9) (100)(0.1)(0.9) = 3
  1. z = ±1: x1 = µ + zσ = 10 + 1(3) = 13 and x2 = µ – zσ = 10 – 1(3) = 7. 68% of the defective cars will fall between seven and 13.
  2. z = ±2: x1 = µ + zσ = 10 + 2(3) = 16 and x2 = µ – zσ = 10 – 2(3) = 4. 95 % of the defective cars will fall between four and 16
  3. z = ±3: x1 = µ + zσ = 10 + 3(3) = 19 and x2 = µ – zσ = 10 – 3(3) = 1. 99.7% of the defective cars will fall between one and 19.
87.
  • n = 190; p = 1 5 1 5 = 0.2; q = 0.8
  • μ = np = (190)(0.2) = 38
  • σ = npq npq = (190)(0.2)(0.8) (190)(0.2)(0.8) = 5.5136
  1. For this problem: P(34 < x < 54) = normalcdf(34,54,48,5.5136) = 0.7641
  2. For this problem: P(54 < x < 64) = normalcdf(54,64,48,5.5136) = 0.0018
  3. For this problem: P(x > 64) = normalcdf(64,1099,48,5.5136) = 0.0000012 (approximately 0)
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