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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 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 (Optional)
    5. 4.4 Geometric Distribution (Optional)
    6. 4.5 Hypergeometric Distribution (Optional)
    7. 4.6 Poisson Distribution (Optional)
    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 (Optional)
    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 (Optional)
    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's 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, and the 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 (Optional)
    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 The Regression Equation
    4. 12.3 Testing the Significance of the Correlation Coefficient (Optional)
    5. 12.4 Prediction (Optional)
    6. 12.5 Outliers
    7. 12.6 Regression (Distance from School) (Optional)
    8. 12.7 Regression (Textbook Cost) (Optional)
    9. 12.8 Regression (Fuel Efficiency) (Optional)
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. Bringing It Together: Homework
    16. References
    17. 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 | Appendix A Review Exercises (Ch 3–13)
  16. B | Appendix 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 Definitions of Statistics, Probability, and Key Terms

1.

Below is a two-way table showing the types of college sports played by men and women.

Soccer Basketball Lacrosse Total
Women 8 8 4 20
Men 4 12 4 20
Total 12 20 8 40
Table 1.28

Given these data, calculate the marginal distributions of college sports for the people surveyed.

2.

Below is a two-way table showing the types of college sports played by men and women.

Soccer Basketball Lacrosse Total
Women 8 8 4 20
Men 4 12 4 20
Total 12 20 8 40
Table 1.29

Given these data, calculate the conditional distributions for the subpopulation of women who play college sports.

Use the following information to answer the next five exercises. Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new viral antibody drug is currently under study. It is given to patients once the virus's symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once they start the treatment. Two researchers each follow a different set of 40 patients with the viral disease from the start of treatment until their deaths. The following data (in months) are collected.

Researcher A3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34

Researcher B3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29

Determine what the key terms refer to in the example for Researcher A.

3.

population

4.

sample

5.

parameter

6.

statistic

7.

variable

1.2 Data, Sampling, and Variation in Data and Sampling

8.

Number of times per week is what type of data?

a. qualitative (categorical); b. quantitative discrete; c. quantitative continuous

Use the following information to answer the next four exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas. The first house in the neighborhood around the park was selected randomly, and then the resident of every eighth house in the neighborhood around the park was interviewed.

9.

The sampling method was

a. simple random; b. systematic; c. stratified; d. cluster

10.

Duration (amount of time) is what type of data?

a. qualitative (categorical); b. quantitative discrete; c. quantitative continuous

11.

The colors of the houses around the park are what kind of data?

a. qualitative (categorical); b. quantitative discrete; c. quantitative continuous

12.

The population is ________.

13.

Table 1.30 contains the total number of deaths worldwide as a result of earthquakes from 2000–2012.

YearTotal Number of Deaths
2000 231
2001 21,357
2002 11,685
2003 33,819
2004 228,802
2005 88,003
2006 6,605
2007 712
2008 88,011
2009 1,790
2010 320,120
2011 21,953
2012 768
Total 823,856
Table 1.30

Use Table 1.30 to answer the following questions.

  1. What is the proportion of deaths between 2007–2012?
  2. What percent of deaths occurred before 2001?
  3. What is the percent of deaths that occurred in 2003 or after 2010?
  4. What is the fraction of deaths that happened before 2012?
  5. What kind of data is the number of deaths?
  6. Earthquakes are quantified according to the amount of energy they produce (examples are 2.1, 5.0, 6.7). What type of data is that?
  7. What contributed to the large number of deaths in 2010? In 2004? Explain.
  8. If you were asked to present these data in an oral presentation, what type of graph would you choose to present and why? Explain what features you would point out on the graph during your presentation.

For the following four exercises, determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience).

14.

A group of test subjects is divided into twelve groups; then four of the groups are chosen at random.

15.

A market researcher polls every tenth person who walks into a store.

16.

The first 50 people who walk into a sporting event are polled on their television preferences.

17.

A computer generates 100 random numbers, and 100 people whose names correspond with the numbers on the list are chosen.


Use the following information to answer the next seven exercises: Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new viral antibody drug is currently under study. It is given to patients once the virus's symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once starting the treatment. Two researchers each follow a different set of 40 patients with the viral disease from the start of treatment until their deaths. The following data (in months) are collected:

Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34

Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29

18.

Complete the tables using the data provided.

Survival Length (in months) Frequency Relative Frequency Cumulative Relative Frequency
.5–6.5
6.5–12.5
12.5–18.5
18.5–24.5
24.5–30.5
30.5–36.5
36.5–42.5
42.5–48.5
Table 1.31 Researcher A
Survival Length (in months) Frequency Relative Frequency Cumulative Relative Frequency
.5–6.5
6.5–12.5
12.5–18.5
18.5–24.5
24.5–30.5
30.5–36.5
36.5-45.5
Table 1.32 Researcher B
19.

Determine what the key term data refers to in the above example for Researcher A.

20.

List two reasons why the data may differ.

21.

Can you tell if one researcher is correct and the other one is incorrect? Why?

22.

Would you expect the data to be identical? Why or why not?

23.

Suggest at least two methods the researchers might use to gather random data.

24.

Suppose that the first researcher conducted his survey by randomly choosing one state in the nation and then randomly picking 40 patients from that state. What sampling method would that researcher have used?

25.

Suppose that the second researcher conducted his survey by choosing 40 patients he knew. What sampling method would that researcher have used? What concerns would you have about this data set, based upon the data collection method?

Use the following data to answer the next five exercises: Two researchers are gathering data on hours of video games played by school-aged children and young adults. They each randomly sample different groups of 150 students from the same school. They collect the following data:

Hours Played per Week Frequency Relative Frequency Cumulative Relative Frequency
0–2 26 .17 .17
2–4 30 .20 .37
4–6 49 .33 .70
6–8 25 .17 .87
8–10 12 .08 .95
10–12 8 .05 1
Table 1.33 Researcher A
Hours Played per Week Frequency Relative Frequency Cumulative Relative Frequency
0–2 48 .32 .32
2–4 51 .34 .66
4–6 24 .16 .82
6–8 12 .08 .90
8–10 11 .07 .97
10–12 4 .03 1
Table 1.34 Researcher B
26.

Give a reason why the data may differ.

27.

Would the sample size be large enough if the population is the students in the school?

28.

Would the sample size be large enough if the population is school-aged children and young adults in the United States?

29.

Researcher A concludes that most students play video games between four and six hours each week. Researcher B concludes that most students play video games between two and four hours each week. Who is correct?

30.

Suppose you were asked to present the data from researchers A and B in an oral presentation. When would a pie graph be appropriate? When would a bar graph more desirable? Explain which features you would point out on each type of graph and what potential display problems you would try to avoid.

31.

As part of a way to reward students for participating in the survey, the researchers gave each student a gift card to a video game store. Would this affect the data if students knew about the award before the study?

Use the following data to answer the next five exercises: A pair of studies was performed to measure the effectiveness of a new software program designed to help stroke patients regain their problem-solving skills. Patients were asked to use the software program twice a day, once in the morning, and once in the evening. The studies observed 200 stroke patients recovering over a period of several weeks. The first study collected the data in Table 1.35. The second study collected the data in Table 1.36.

Group Showed Improvement No Improvement Deterioration
Used program 142 43 15
Did not use program 72 110 18
Table 1.35
Group Showed Improvement No Improvement Deterioration
Used program 105 74 19
Did not use program 89 99 12
Table 1.36
32.

Given what you know, which study is correct?

33.

The first study was performed by the company that designed the software program. The second study was performed by the American Medical Association. Which study is more reliable?

34.

Both groups that performed the study concluded that the software works. Is this accurate?

35.

The company takes the two studies as proof that their software causes mental improvement in stroke patients. Is this a fair statement?

36.

Patients who used the software were also a part of an exercise program whereas patients who did not use the software were not. Does this change the validity of the conclusions from Exercise 1.34?

37.

Is a sample size of 1,000 a reliable measure for a population of 5,000?

38.

Is a sample of 500 volunteers a reliable measure for a population of 2,500?

39.

A question on a survey reads: "Do you prefer the delicious taste of Brand X or the taste of Brand Y?" Is this a fair question?

40.

Is a sample size of two representative of a population of five?

41.

Is it possible for two experiments to be well run with similar sample sizes to get different data?

1.3 Frequency, Frequency Tables, and Levels of Measurement

42.

What type of measure scale is being used? Nominal, ordinal, interval or ratio.

  1. High school soccer players classified by their athletic ability: superior, average, above average
  2. Baking temperatures for various main dishes: 350, 400, 325, 250, 300
  3. The colors of crayons in a 24-crayon box
  4. Social security numbers
  5. Incomes measured in dollars
  6. A satisfaction survey of a social website by number: 1 = very satisfied, 2 = somewhat satisfied, 3 = not satisfied
  7. Preferred TV shows: comedy, drama, science fiction, sports, news
  8. Time of day on an analog watch
  9. The distance in miles to the closest grocery store
  10. The dates 1066, 1492, 1644, 1947, and 1944
  11. The heights of 21–65-year-old women
  12. Common letter grades: A, B, C, D, and F

1.4 Experimental Design and Ethics

43.

Design an experiment. Identify the explanatory and response variables. Describe the population being studied and the experimental units. Explain the treatments that will be used and how they will be assigned to the experimental units. Describe how blinding and placebos may be used to counter the power of suggestion.

44.

Discuss potential violations of the rule requiring informed consent.

  1. Inmates in a correctional facility are offered good behavior credit in return for participation in a study.
  2. A research study is designed to investigate a new children’s allergy medication.
  3. Participants in a study are told that the new medication being tested is highly promising, but they are not told that only a small portion of participants will receive the new medication. Others will receive placebo treatments and traditional treatments.
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