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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 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.

mean = 4 hours; standard deviation = 1.2 hours; sample size = 16

3.

a. Check student's solution.
b. 3.5, 4.25, 0.2441

5.

The fact that the two distributions are different accounts for the different probabilities.

7.

0.3345

9.

7,833.92

11.

0.0089

13.

7,326.49

15.

77.45%

17.

0.4207

19.

3,888.5

21.

0.8186

23.

5

25.

0.9772

27.

The sample size, n, gets larger.

29.

49

31.

26.00

33.

0.1587

35.

1,000

37.
  1. U(24, 26), 25, 0.5774
  2. N(25, 0.0577)
  3. 0.0416
39.

0.0003

41.

25.07

43.
  1. N(2,500, 5.7735)
  2. 0
45.

2,507.40

47.
  1. 10
  2. 1 10 1 10
49.

N ( 10,  10 8 ) ( 10,  10 8 )

51.

0.7799

53.

1.69

55.

0.0072

57.

391.54

59.

405.51

61.
  1. Χ = amount of change students carry
  2. Χ ~ E(0.88, 0.88)
  3. X ¯ X ¯ = average amount of change carried by a sample of 25 sstudents.
  4. X ¯ X ¯ ~ N(0.88, 0.176)
  5. 0.0819
  6. 0.1882
  7. The distributions are different. Part a is exponential and part b is normal.
63.
  1. length of time for an individual to complete IRS form 1040, in hours.
  2. mean length of time for a sample of 36 taxpayers to complete IRS form 1040, in hours.
  3. N ( 10.53,  1 3 ) ( 10.53,  1 3 )
  4. Yes. I would be surprised, because the probability is almost 0.
  5. No. I would not be totally surprised because the probability is 0.2312
65.
  1. the length of a song, in minutes, in the collection
  2. U(2, 3.5)
  3. the average length, in minutes, of the songs from a sample of five albums from the collection
  4. N(2.75, 0.0660)
  5. 2.71 minutes
  6. 0.09 minutes
67.
  1. True. The mean of a sampling distribution of the means is approximately the mean of the data distribution.
  2. True. According to the Central Limit Theorem, the larger the sample, the closer the sampling distribution of the means becomes normal.
  3. The standard deviation of the sampling distribution of the means will decrease making it approximately the same as the standard deviation of X as the sample size increases.
69.
  1. X = the yearly income of someone in a third world country
  2. the average salary from samples of 1,000 residents of a third world country
  3. X ¯ X ¯ N ( 2000,  8000 1000 ) ( 2000,  8000 1000 )
  4. Very wide differences in data values can have averages smaller than standard deviations.
  5. The distribution of the sample mean will have higher probabilities closer to the population mean.
    P(2000 < X ¯ X ¯ < 2100) = 0.1537
    P(2100 < X ¯ X ¯ < 2200) = 0.1317
71.

b

73.
  1. the total length of time for nine criminal trials
  2. N(189, 21)
  3. 0.0432
  4. 162.09; ninety percent of the total nine trials of this type will last 162 days or more.
75.
  1. X = the salary of one elementary school teacher in the district
  2. X ~ N(44,000, 6,500)
  3. ΣX ~ sum of the salaries of ten elementary school teachers in the sample
  4. ΣX ~ N(44000, 20554.80)
  5. 0.9742
  6. $52,330.09
  7. 466,342.04
  8. Sampling 70 teachers instead of ten would cause the distribution to be more spread out. It would be a more symmetrical normal curve.
  9. If every teacher received a $3,000 raise, the distribution of X would shift to the right by $3,000. In other words, it would have a mean of $47,000.
77.
  1. X = the closing stock prices for U.S. semiconductor manufacturers
  2. i. $20.71; ii. $17.31; iii. 35
  3. Exponential distribution, Χ ~ Exp ( 1 20.71 ) ( 1 20.71 )
  4. Answers will vary.
  5. i. $20.71; ii. $11.14
  6. Answers will vary.
  7. Answers will vary.
  8. Answers will vary.
  9. N ( 20.71,  17.31 5 ) ( 20.71,  17.31 5 )
79.

b

81.

b

83.

a

85.
  1. 0
  2. 0.1123
  3. 0.0162
  4. 0.0003
  5. 0.0268
87.
  1. Check student’s solution.
  2. X ¯ X ¯ ~ N ( 60,  9 25 ) ( 60,  9 25 )
  3. 0.5000
  4. 59.06
  5. 0.8536
  6. 0.1333
  7. N(1500, 45)
  8. 1530.35
  9. 0.6877
89.
  1. $52,330
  2. $46,634
91.
  • We have μ = 17, σ = 0.8, x ¯ x ¯ = 16.7, and n = 30. To calculate the probability, we use normalcdf(lower, upper, μ, σ n σ n ) = normalcdf ( E99,16.7,17, 0.8 30 ) ( E99,16.7,17, 0.8 30 ) = 0.0200.
  • If the process is working properly, then the probability that a sample of 30 batteries would have at most 16.7 lifetime hours is only 2%. Therefore, the class was justified to question the claim.
93.
  1. For the sample, we have n = 100, x ¯ x ¯ = 0.862, s = 0.05
  2. Σ x ¯ Σ x ¯ = 85.65, Σs = 5.18
  3. normalcdf(396.9,E99,(465)(0.8565),(0.05)( 465 465 )) ≈ 1
  4. Since the probability of a sample of size 465 having at least a mean sum of 396.9 is appproximately 1, we can conclude that Mars is correctly labeling their M&M packages.
95.

Use normalcdf ( E99,1.1,1, 1 70 ) ( E99,1.1,1, 1 70 ) = 0.7986. This means that there is an 80% chance that the service time will be less than 1.1 hours. It could be wise to schedule more time since there is an associated 20% chance that the maintenance time will be greater than 1.1 hours.

97.

We assume that the weights of coins are normally distributed in the population. Since we have normalcdf ( 5.111,5.291,5.201, 0.065 280 ) ( 5.111,5.291,5.201, 0.065 280 ) ≈ 0.8338, we expect (1 – 0.8338)280 ≈ 47 coins to be rejected.

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