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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.
  1. P(L′) = P(S)
  2. P(M OR S)
  3. P(F AND L)
  4. P(M|L)
  5. P(L|M)
  6. P(S|F)
  7. P(F|L)
  8. P(F OR L)
  9. P(M AND S)
  10. P(F)
3.

P(N) = 15 42 15 42 = 5 14 5 14 = 0.36

5.

P(C) = 5 42 5 42 = 0.12

7.

P(G) = 20 150 20 150 = 2 15 2 15 = 0.13

9.

P(R) = 22 150 22 150 = 11 75 11 75 = 0.15

11.

P(O) = 150-22-38-20-28-26 150 150-22-38-20-28-26 150 = 16 150 16 150 = 8 75 8 75 = 0.11

13.

P(E) = 47 194 47 194 = 0.24

15.

P(N) = 23 194 23 194 = 0.12

17.

P(S) = 12 194 12 194 = 6 97 6 97 = 0.06

19.

13 52 13 52 = 1 4 1 4 = 0.25

21.

3 6 3 6 = 1 2 1 2 = 0.5

23.

P(R)= 4 8 =0.5 P(R)= 4 8 =0.5

25.

P(O OR H)

27.

P(H|I)

29.

P(N|O)

31.

P(I OR N)

33.

P(I)

35.

The likelihood that an event will occur given that another event has already occurred.

37.

1

39.

the probability of landing on an even number or a multiple of three

41.

P(J) = 0.3

43.

P(Q AND R) = P(Q)P(R)

0.1 = (0.4)P(R)

P(R) = 0.25

45.

0.376

47.

C|L means, given the person chosen is a Latino Californian, the person is a registered voter who prefers life in prison without parole for a person convicted of first degree murder.

49.

L AND C is the event that the person chosen is a Latino California registered voter who prefers life without parole over the death penalty for a person convicted of first degree murder.

51.

0.6492

53.

No, because P(L AND C) does not equal 0.

55.

P(musician is a male AND had private instruction) = 15 130 15 130 = 3 26 3 26 = 0.12

57.

P(being a female musician AND learning music in school) = 38 130 38 130 = 19 65 19 65 = 0.29

P(being a female musician)P(learning music in school) = ( 72 130 )( 62 130 ) ( 72 130 )( 62 130 ) = 4,464 16,900 4,464 16,900 = 1,116 4,225 1,116 4,225 = 0.26

No, they are not independent because P(being a female musician AND learning music in school) is not equal to P(being a female musician)P(learning music in school).

58.
This is a tree diagram with two branches. The first branch, labeled Cancer, shows two lines: 0.4567 C and 0.5433 C'. The second branch is labeled False Positive. From C, there are two lines: 0 P and 1 P'. From C', there are two lines: 0.51 P and 0.49 P'.
Figure 3.15
60.

35,065100,45035,065100,450

62.

To pick one person from the study who is Japanese American AND smokes 21 to 30 cigarettes per day means that the person has to meet both criteria: both Japanese American and smokes 21 to 30 cigarettes. The sample space should include everyone in the study. The probability is 4,715100,4504,715100,450.

64.

To pick one person from the study who is Japanese American given that person smokes 21-30 cigarettes per day, means that the person must fulfill both criteria and the sample space is reduced to those who smoke 21-30 cigarettes per day. The probability is 471515,273471515,273.

67.
  1. You can't calculate the joint probability knowing the probability of both events occurring, which is not in the information given; the probabilities should be multiplied, not added; and probability is never greater than 100%
  2. A home run by definition is a successful hit, so he has to have at least as many successful hits as home runs.
69.

0

71.

0.3571

73.

0.2142

75.

Physician (83.7)

77.

83.7 − 79.6 = 4.1

79.

P(Occupation < 81.3) = 0.5

81.
  1. The Forum Research surveyed 1,046 Torontonians.
  2. 58%
  3. 42% of 1,046 = 439 (rounding to the nearest integer)
  4. 0.57
  5. 0.60.
83.
  1. P(Betting on two line that touch each other on the table) = 6 38 6 38
  2. P(Betting on three numbers in a line) = 3 38 3 38
  3. P(Bettting on one number) = 1 38 1 38
  4. P(Betting on four number that touch each other to form a square) = 4 38 4 38
  5. P(Betting on two number that touch each other on the table ) = 2 38 2 38
  6. P(Betting on 0-00-1-2-3) = 5 38 5 38
  7. P(Betting on 0-1-2; or 0-00-2; or 00-2-3) = 3 38 3 38
85.
  1. {G1, G2, G3, G4, G5, Y1, Y2, Y3}
  2. 5 8 5 8
  3. 2 3 2 3
  4. 2 8 2 8
  5. 6 8 6 8
  6. No, because P(G AND E) does not equal 0.
87.

NOTE

The coin toss is independent of the card picked first.

  1. {(G,H) (G,T) (B,H) (B,T) (R,H) (R,T)}
  2. P(A) = P(blue)P(head) = ( 3 10 ) ( 3 10 ) ( 1 2 ) ( 1 2 ) = 3 20 3 20
  3. Yes, A and B are mutually exclusive because they cannot happen at the same time; you cannot pick a card that is both blue and also (red or green). P(A AND B) = 0
  4. No, A and C are not mutually exclusive because they can occur at the same time. In fact, C includes all of the outcomes of A; if the card chosen is blue it is also (red or blue). P(A AND C) = P(A) = 3 20 3 20
89.
  1. S = {(HHH), (HHT), (HTH), (HTT), (THH), (THT), (TTH), (TTT)}
  2. 4 8 4 8
  3. Yes, because if A has occurred, it is impossible to obtain two tails. In other words, P(A AND B) = 0.
91.
  1. If Y and Z are independent, then P(Y AND Z) = P(Y)P(Z), so P(Y OR Z) = P(Y) + P(Z) - P(Y)P(Z).
  2. 0.5
93.

iii i iv ii

95.
  1. P(R) = 0.44
  2. P(R|E) = 0.56
  3. P(R|O) = 0.31
  4. No, whether the money is returned is not independent of which class the money was placed in. There are several ways to justify this mathematically, but one is that the money placed in economics classes is not returned at the same overall rate; P(R|E) ≠ P(R).
  5. No, this study definitely does not support that notion; in fact, it suggests the opposite. The money placed in the economics classrooms was returned at a higher rate than the money place in all classes collectively; P(R|E) > P(R).
97.
  1. P(type O OR Rh-) = P(type O) + P(Rh-) - P(type O AND Rh-)

    0.52 = 0.43 + 0.15 - P(type O AND Rh-); solve to find P(type O AND Rh-) = 0.06

    6% of people have type O, Rh- blood

  2. P(NOT(type O AND Rh-)) = 1 - P(type O AND Rh-) = 1 - 0.06 = 0.94

    94% of people do not have type O, Rh- blood

99.
  1. Let C = be the event that the cookie contains chocolate. Let N = the event that the cookie contains nuts.
  2. P(C OR N) = P(C) + P(N) - P(C AND N) = 0.36 + 0.12 - 0.08 = 0.40
  3. P(NEITHER chocolate NOR nuts) = 1 - P(C OR N) = 1 - 0.40 = 0.60
101.

0

103.

10 67 10 67

105.

10 34 10 34

107.

d

109.
  1. Race and Sex 1–14 15–24 25–64 over 64 TOTALS
    white, male 210 3,360 13,610 4,870 22,050
    white, female 80 580 3,380 890 4,930
    black, male 10 460 1,060 140 1,670
    black, female 0 40 270 20 330
    all others 100
    TOTALS 310 4,650 18,780 6,020 29,760
    Table 3.26
  2. Race and Sex 1–14 15–24 25–64 over 64 TOTALS
    white, male 210 3,360 13,610 4,870 22,050
    white, female 80 580 3,380 890 4,930
    black, male 10 460 1,060 140 1,670
    black, female 0 40 270 20 330
    all others 10 210 460 100 780
    TOTALS 310 4,650 18,780 6,020 29,760
    Table 3.27
  3. 22,050 29,760 22,050 29,760
  4. 330 29,760 330 29,760
  5. 2,000 29,760 2,000 29,760
  6. 23720 ( 29760-780 ) = 23720 28980 23720 ( 29760-780 ) = 23720 28980
  7. 5010 ( 6020-100 ) = 5010 5920 5010 ( 6020-100 ) = 5010 5920
111.

b

113.
  1. 26 106 26 106
  2. 33 106 33 106
  3. 21 106 21 106
  4. ( 26 106 ) ( 26 106 ) + ( 33 106 ) ( 33 106 ) - ( 21 106 ) ( 21 106 ) = ( 38 106 ) ( 38 106 )
  5. 21 33 21 33
115.

a

118.
  1. P(C) = 0.4567
  2. not enough information
  3. not enough information
  4. No, because over half (0.51) of men have at least one false positive text
120.
  1. P(J OR K) = P(J) + P(K) − P(J AND K); 0.45 = 0.18 + 0.37 - P(J AND K); solve to find P(J AND K) = 0.10
  2. P(NOT (J AND K)) = 1 - P(J AND K) = 1 - 0.10 = 0.90
  3. P(NOT (J OR K)) = 1 - P(J OR K) = 1 - 0.45 = 0.55
121.
  1. This is a tree diagram with branches showing probabilities of each draw. The first branch shows two lines: 5/8 Green and 3/8 Yellow. The second branch has a set of two lines (5/8 Green and 3/8 Yellow) for each line of the first branch.
    Figure 3.16
  2. P(GG) = ( 5 8 )( 5 8 ) ( 5 8 )( 5 8 ) = 25 64 25 64
  3. P(at least one green) = P(GG) + P(GY) + P(YG) = 25 64 25 64 + 15 64 15 64 + 15 64 15 64 = 55 64 55 64
  4. P(G|G) = 5 8 5 8
  5. Yes, they are independent because the first card is placed back in the bag before the second card is drawn; the composition of cards in the bag remains the same from draw one to draw two.
123.
  1. <2020–64>64Totals
    Female 0.0244 0.3954 0.0661 0.486
    Male 0.0259 0.4186 0.0695 0.514
    Totals 0.0503 0.8140 0.1356 1
    Table 3.28
  2. P(F) = 0.486
  3. P(>64|F) = 0.1361
  4. P(>64 and F) = P(F) P(>64|F) = (0.486)(0.1361) = 0.0661
  5. P(>64|F) is the percentage of female drivers who are 65 or older and P(>64 and F) is the percentage of drivers who are female and 65 or older.
  6. P(>64) = P(>64 and F) + P(>64 and M) = 0.1356
  7. No, being female and 65 or older are not mutually exclusive because they can occur at the same time P(>64 and F) = 0.0661.
125.
  1. Car, Truck or Van Walk Public Transportation Other Totals
    Alone 0.7318
    Not Alone 0.1332
    Totals 0.8650 0.0390 0.0530 0.0430 1
    Table 3.29
  2. If we assume that all walkers are alone and that none from the other two groups travel alone (which is a big assumption) we have: P(Alone) = 0.7318 + 0.0390 = 0.7708.
  3. Make the same assumptions as in (b) we have: (0.7708)(1,000) = 771
  4. (0.1332)(1,000) = 133
127.

The completed contingency table is as follows:

Homosexual/Bisexual IV Drug User* Heterosexual Contact Other Totals
Female 0 70 136 49 255
Male 2,146 463 60 135 2,804
Totals 2,146 533 196 184 3,059
Table 3.30 * includes homosexual/bisexual IV drug users
  1. 255 3059 255 3059
  2. 196 3059 196 3059
  3. 718 3059 718 3059
  4. 0
  5. 463 3059 463 3059
  6. 136 196 136 196
  7. Figure 3.17
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