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Introductory Statistics

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Introductory StatisticsIndex
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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
    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
Symbols
α 9.4 Rare Events, the Sample, Decision and Conclusion
A
absolute value of a residual 12.3 The Regression Equation
alternative hypothesis 9.1 Null and Alternative Hypotheses
Area to the left 6.2 Using the Normal Distribution
Area to the right 6.2 Using the Normal Distribution
assumption 9.4 Rare Events, the Sample, Decision and Conclusion
average 1.1 Definitions of Statistics, Probability, and Key Terms
B
balanced design 13.3 Facts About the F Distribution
bar graph 1.2 Data, Sampling, and Variation in Data and Sampling
Bernoulli Trial 4.3 Binomial Distribution
binomial distribution 7.3 Using the Central Limit Theorem, 8.3 A Population Proportion, 9.3 Distribution Needed for Hypothesis Testing
binomial probability distribution 4.3 Binomial Distribution
bivariate Introduction
Blinding 1.4 Experimental Design and Ethics
Box plots 2.4 Box Plots
box-and-whisker plots 2.4 Box Plots
box-whisker plots 2.4 Box Plots
C
categorical data 1.2 Data, Sampling, and Variation in Data and Sampling
Categorical variables 1.1 Definitions of Statistics, Probability, and Key Terms
central limit theorem Introduction, 7.1 The Central Limit Theorem for Sample Means (Averages), 7.3 Using the Central Limit Theorem, 9.5 Additional Information and Full Hypothesis Test Examples
central limit theorem for means 7.1 The Central Limit Theorem for Sample Means (Averages)
central limit theorem for sums 7.2 The Central Limit Theorem for Sums
chi-square distribution 11.1 Facts About the Chi-Square Distribution
coefficient of determination 12.3 The Regression Equation
Cohen's d 10.1 Two Population Means with Unknown Standard Deviations
complement 3.1 Terminology
conditional probability 3.1 Terminology, 5.2 The Uniform Distribution
confidence interval Introduction, 8.2 A Single Population Mean using the Student t Distribution
confidence intervals 8.3 A Population Proportion, Introduction
confidence level 8.1 A Single Population Mean using the Normal Distribution, 8.3 A Population Proportion
contingency table 3.4 Contingency Tables, 11.3 Test of Independence
continuity correction factor 7.3 Using the Central Limit Theorem
continuous 1.2 Data, Sampling, and Variation in Data and Sampling
continuous random variable 5.3 The Exponential Distribution
control group 1.4 Experimental Design and Ethics
critical value 6.2 Using the Normal Distribution
cumulative distribution function (CDF) 5.3 The Exponential Distribution
Cumulative relative frequency 1.3 Frequency, Frequency Tables, and Levels of Measurement
D
data 1.1 Definitions of Statistics, Probability, and Key Terms, 1.1 Definitions of Statistics, Probability, and Key Terms
degrees of freedom 8.2 A Single Population Mean using the Student t Distribution
degrees of freedom (df) 10.1 Two Population Means with Unknown Standard Deviations
descriptive statistics 1.1 Definitions of Statistics, Probability, and Key Terms
discrete 1.2 Data, Sampling, and Variation in Data and Sampling
double-blind experiment 1.4 Experimental Design and Ethics
E
Empirical Rule 6.1 The Standard Normal Distribution, Introduction
equal standard deviations 13.1 One-Way ANOVA
Equally likely 3.1 Terminology, 5.2 The Uniform Distribution
error bound 8.3 A Population Proportion
error bound for a population mean 8.1 A Single Population Mean using the Normal Distribution, 8.2 A Single Population Mean using the Student t Distribution
event 3.1 Terminology
expected value 4.2 Mean or Expected Value and Standard Deviation, 4.2 Mean or Expected Value and Standard Deviation
expected values 11.2 Goodness-of-Fit Test
experiment 3.1 Terminology
experimental unit 1.4 Experimental Design and Ethics
explanatory variable 1.4 Experimental Design and Ethics
exponential distribution 5.3 The Exponential Distribution, 7.3 Using the Central Limit Theorem
extrapolation 12.5 Prediction
F
F distribution 13.2 The F Distribution and the F-Ratio
F ratio 13.2 The F Distribution and the F-Ratio
fair 3.1 Terminology
first quartile 2.3 Measures of the Location of the Data
frequency 1.3 Frequency, Frequency Tables, and Levels of Measurement, 2.2 Histograms, Frequency Polygons, and Time Series Graphs
G
geometric distribution 4.4 Geometric Distribution
goodness-of-fit test 11.2 Goodness-of-Fit Test
H
histogram 2.2 Histograms, Frequency Polygons, and Time Series Graphs
hypergeometric experiment 4 Chapter Review
hypergeometric probability 4.5 Hypergeometric Distribution
hypotheses 9.1 Null and Alternative Hypotheses
hypothesis test 9.3 Distribution Needed for Hypothesis Testing, 9.5 Additional Information and Full Hypothesis Test Examples, 9 Chapter Review
hypothesis testing Introduction
I
independent 3.2 Independent and Mutually Exclusive Events, 3.3 Two Basic Rules of Probability
Independent groups Introduction
inferential statistics 1.1 Definitions of Statistics, Probability, and Key Terms, Introduction
influential points 12.6 Outliers
informed consent 1.4 Experimental Design and Ethics
Institutional Review Boards (IRB) 1.4 Experimental Design and Ethics
interpolation 12.5 Prediction
interquartile range 2.3 Measures of the Location of the Data
interval scale 1.3 Frequency, Frequency Tables, and Levels of Measurement
L
law of large numbers 3.1 Terminology, 7.3 Using the Central Limit Theorem
Least-Squares Line 12.3 The Regression Equation
least-squares regression line 12.3 The Regression Equation
level of measurement 1.3 Frequency, Frequency Tables, and Levels of Measurement
Line of Best Fit 12.3 The Regression Equation
linear regression 12.2 Scatter Plots
long-term relative frequency 3.1 Terminology
lurking variables 1.4 Experimental Design and Ethics
M
margin of error Introduction
matched pairs Introduction
mean 1.1 Definitions of Statistics, Probability, and Key Terms, 1.1 Definitions of Statistics, Probability, and Key Terms, 2.5 Measures of the Center of the Data, 4.2 Mean or Expected Value and Standard Deviation, Introduction, 7.1 The Central Limit Theorem for Sample Means (Averages), 7.3 Using the Central Limit Theorem
mean square 13.2 The F Distribution and the F-Ratio
median 2.3 Measures of the Location of the Data, 2.5 Measures of the Center of the Data
mode 2.5 Measures of the Center of the Data
multivariate Introduction
mutually exclusive 3.2 Independent and Mutually Exclusive Events, 3.3 Two Basic Rules of Probability
N
nominal scale 1.3 Frequency, Frequency Tables, and Levels of Measurement
normal approximation to the binomial 7.3 Using the Central Limit Theorem
normal distribution 8.2 A Single Population Mean using the Student t Distribution, 8.3 A Population Proportion, 9.3 Distribution Needed for Hypothesis Testing, 10.2 Two Population Means with Known Standard Deviations
normally distributed 7.1 The Central Limit Theorem for Sample Means (Averages), 7.2 The Central Limit Theorem for Sums, 9.3 Distribution Needed for Hypothesis Testing
null hypothesis 9.1 Null and Alternative Hypotheses, 9.4 Rare Events, the Sample, Decision and Conclusion, 9.4 Rare Events, the Sample, Decision and Conclusion, 9.4 Rare Events, the Sample, Decision and Conclusion
Numerical variables 1.1 Definitions of Statistics, Probability, and Key Terms
O
observed values 11.2 Goodness-of-Fit Test
ordinal scale 1.3 Frequency, Frequency Tables, and Levels of Measurement
outcome 3.1 Terminology
outlier 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs, 2.3 Measures of the Location of the Data
outliers 12.6 Outliers
P
p-value 9.4 Rare Events, the Sample, Decision and Conclusion, 9.5 Additional Information and Full Hypothesis Test Examples
paired data set 2.2 Histograms, Frequency Polygons, and Time Series Graphs
parameter 1.1 Definitions of Statistics, Probability, and Key Terms, Introduction
Pareto chart 1.2 Data, Sampling, and Variation in Data and Sampling
Pearson 1.1 Definitions of Statistics, Probability, and Key Terms
percentile 7.2 The Central Limit Theorem for Sums
percentiles 2.3 Measures of the Location of the Data
pie chart 1.2 Data, Sampling, and Variation in Data and Sampling
placebo 1.4 Experimental Design and Ethics
point estimate Introduction
Poisson probability distribution 4.6 Poisson Distribution, 4 Chapter Review
population 1.1 Definitions of Statistics, Probability, and Key Terms, 1.2 Data, Sampling, and Variation in Data and Sampling
population variance 11.6 Test of a Single Variance
potential outlier 12.6 Outliers
Probability 1.1 Definitions of Statistics, Probability, and Key Terms, 3.1 Terminology
probability density function Introduction
probability distribution function 4.1 Probability Distribution Function (PDF) for a Discrete Random Variable
proportion 1.1 Definitions of Statistics, Probability, and Key Terms
Q
Qualitative data 1.2 Data, Sampling, and Variation in Data and Sampling
quantitative continuous data 1.2 Data, Sampling, and Variation in Data and Sampling
Quantitative data 1.2 Data, Sampling, and Variation in Data and Sampling
quantitative discrete data 1.2 Data, Sampling, and Variation in Data and Sampling
quartiles 2.3 Measures of the Location of the Data, 2.3 Measures of the Location of the Data
R
random assignment 1.4 Experimental Design and Ethics
random variable Introduction, 10.1 Two Population Means with Unknown Standard Deviations, 10.2 Two Population Means with Known Standard Deviations
ratio scale 1.3 Frequency, Frequency Tables, and Levels of Measurement
relative frequency 1.3 Frequency, Frequency Tables, and Levels of Measurement, 2.2 Histograms, Frequency Polygons, and Time Series Graphs
replacement 3.2 Independent and Mutually Exclusive Events
representative sample 1.1 Definitions of Statistics, Probability, and Key Terms
residual 12.3 The Regression Equation
response variable 1.4 Experimental Design and Ethics
S
sample 1.1 Definitions of Statistics, Probability, and Key Terms
sample mean 7.1 The Central Limit Theorem for Sample Means (Averages)
sample size 7.1 The Central Limit Theorem for Sample Means (Averages), 7.2 The Central Limit Theorem for Sums
sample space 3.1 Terminology, 3.3 Two Basic Rules of Probability, 3.5 Tree and Venn Diagrams
samples 1.2 Data, Sampling, and Variation in Data and Sampling
sampling 1.1 Definitions of Statistics, Probability, and Key Terms
sampling distribution 2.5 Measures of the Center of the Data
sampling variability of a statistic 2.7 Measures of the Spread of the Data
simple random sample 9.3 Distribution Needed for Hypothesis Testing
single population mean 9.3 Distribution Needed for Hypothesis Testing
single population proportion 9.3 Distribution Needed for Hypothesis Testing
standard deviation 2.7 Measures of the Spread of the Data, 8.2 A Single Population Mean using the Student t Distribution, 9.3 Distribution Needed for Hypothesis Testing, 9.3 Distribution Needed for Hypothesis Testing, 9.4 Rare Events, the Sample, Decision and Conclusion, 9.5 Additional Information and Full Hypothesis Test Examples
standard error 10.1 Two Population Means with Unknown Standard Deviations
standard error of the mean. 7.1 The Central Limit Theorem for Sample Means (Averages)
standard normal distribution 6.1 The Standard Normal Distribution
statistic 1.1 Definitions of Statistics, Probability, and Key Terms
statistics 1.1 Definitions of Statistics, Probability, and Key Terms
Student's t-distribution 8.2 A Single Population Mean using the Student t Distribution, 9.3 Distribution Needed for Hypothesis Testing, 9.3 Distribution Needed for Hypothesis Testing
Sum of Squared Errors (SSE) 12.3 The Regression Equation
sum of squares 13.2 The F Distribution and the F-Ratio
T
test for homogeneity 11.4 Test for Homogeneity
test of a single variance 11.6 Test of a Single Variance
test of independence 11.3 Test of Independence
test statistic 10.2 Two Population Means with Known Standard Deviations
The standard deviation 10.2 Two Population Means with Known Standard Deviations
third quartile 2.3 Measures of the Location of the Data
treatments 1.4 Experimental Design and Ethics
tree diagram 3.5 Tree and Venn Diagrams
Type I error 9.2 Outcomes and the Type I and Type II Errors, 9.4 Rare Events, the Sample, Decision and Conclusion
Type II error 9.2 Outcomes and the Type I and Type II Errors
U
unfair 3.1 Terminology
uniform distribution 7.3 Using the Central Limit Theorem
V
variable 1.1 Definitions of Statistics, Probability, and Key Terms
variance 2.7 Measures of the Spread of the Data
Variance between samples 13.2 The F Distribution and the F-Ratio
Variance within samples 13.2 The F Distribution and the F-Ratio
variances 13.1 One-Way ANOVA
Variation 1.2 Data, Sampling, and Variation in Data and Sampling
Venn diagram 3.5 Tree and Venn Diagrams
Z
z-score 8.2 A Single Population Mean using the Student t Distribution
z-scores 6.1 The Standard Normal Distribution
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