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  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.

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.

0.1186

55.
  1. Check student’s solution.
  2. 3, 0.1979
57.

0.154

58.

0.874

59.

0.693

60.

0.346

61.

0.110

62.

0.946

63.

0.071

64.

0.347

66.

c

68.
  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.
70.
  1. iv
  2. Kyle’s blood pressure is equal to 125 + (1.75)(14) = 149.5.
72.

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).
75.

d

77.
  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
79.
  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.
81.
  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
83.
  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
85.
  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.
88.
  • 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+=10+1(3)=13z=±1:x1=µ+=10+1(3)=13 and x2=µ=101(3)=7.68%x2=µ=101(3)=7.68% of the defective cars will fall between seven and 13.
  2. z=±2: x1=µ+=10+2(3)=16z=±2:x1=µ+=10+2(3)=16 and x2=µ=102(3)=4. 95 %x2=µ=102(3)=4. 95 % of the defective cars will fall between four and 16
  3. z=±3: x1=µ+ =10+3(3)=19z=±3:x1=µ+=10+3(3)=19 and x2=µ=103(3)=1. 99.7%x2=µ=103(3)=1. 99.7% of the defective cars will fall between one and 19.
90.
  • 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) = 0.7641
  2. For this problem: P(54 < x < 64) = 0.0018
  3. For this problem: P(x > 64) = 0.0000012 (approximately 0)
92.
  1. 24.5
  2. 3.5
  3. Yes
  4. 0.67
93.
  1. 63
  2. 2.5
  3. Yes
  4. 0.88
94.

0.02

95.

0.37

96.

0.50

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