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MATH-201: Elements of Statistics and Probability

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MATH-201: Elements of Statistics and Probability

The use of probability techniques, hypothesis testing, and predictive techniques to facilitate decision-making. Topics include descriptive statistics; probability and sampling distributions; statistical inference; correlation and linear regression; analysis of variance, chi-square and t-tests; and application of technology for statistical analysis including the interpretation of the relevance of the statistical findings.

Statistics
Publisher
Lake Tahoe Community College
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 141 sections
  1. 01: Sampling and Data
  2. 1.1: Introduction
  3. 1.2: Definitions of Statistics Probability and Key Terms
  4. 1.3: Data Sampling and Variation in Data and Sampling
  5. 1.4: Frequency Frequency Tables and Levels of Measurement
  6. 1.5: Experimental Design and Ethics
  7. 1.6: Data Collection Experiment (Worksheet)
  8. 1.7: Sampling Experiment (Worksheet)
  9. 1.8: Sampling and Data (Exercises)
  10. 02: Descriptive Statistics
  11. 2.01: Prelude to Descriptive Statistics
  12. 2.02: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
  13. 2.03: Histograms, Frequency Polygons, and Time Series Graphs
  14. 2.04: Measures of the Location of the Data
  15. Measures of the Location of the Data (Exercises)
  16. 2.05: Box Plots
  17. 2.06: Measures of the Center of the Data
  18. 2.07: Skewness and the Mean, Median, and Mode
  19. 2.08: Measures of the Spread of the Data
  20. 2.09: Descriptive Statistics (Worksheet)
  21. 2.10: Descriptive Statistics (Exercises)
  22. 03: Probability Topics
  23. 3.1: Introduction
  24. 3.2: Terminology
  25. 3.3: Independent and Mutually Exclusive Events
  26. 3.4: Two Basic Rules of Probability
  27. 3.5: Contingency Tables
  28. 3.6: Tree and Venn Diagrams
  29. 3.7: Probability Topics (Worksheet)
  30. 3.8: Probability Topics (Exericses)
  31. 04: Discrete Random Variables
  32. 4.01: Prelude to Discrete Random Variables
  33. 4.02: Probability Distribution Function (PDF) for a Discrete Random Variable
  34. 4.03: Mean or Expected Value and Standard Deviation
  35. 4.04: Binomial Distribution
  36. 4.05: Geometric Distribution
  37. 4.06: Hypergeometric Distribution
  38. 4.07: Poisson Distribution
  39. 4.08: Discrete Distribution (Playing Card Experiment)
  40. 4.09: Discrete Distribution (Lucky Dice Experiment)
  41. 4.10: Discrete Random Variables (Exercises)
  42. 05: Continuous Random Variables
  43. 5.1: Introduction
  44. 5.2: Continuous Probability Functions
  45. 5.3: The Uniform Distribution
  46. 5.4: The Exponential Distribution
  47. 5.5: Continuous Distribution (Worksheet)
  48. 5.6: Continuous Random Variables (Exercises)
  49. 5.7: Exercises
  50. 06: The Normal Distribution
  51. 6.1: Prelude to The Normal Distribution
  52. 6.2: The Standard Normal Distribution
  53. The Standard Normal Distribution (Exercises)
  54. 6.3: Using the Normal Distribution
  55. 6.4: Normal Distribution - Lap Times (Worksheet)
  56. 6.5: Normal Distribution - Pinkie Length (Worksheet)
  57. 6.6: The Normal Distribution (Exercises)
  58. 07: The Central Limit Theorem
  59. 7.1: Prelude to the Central Limit Theorem
  60. 7.2: The Central Limit Theorem for Sample Means (Averages)
  61. The Central Limit Theorem for Sample Means (Exercises)
  62. 7.3: The Central Limit Theorem for Sums
  63. 7.4: Using the Central Limit Theorem
  64. Using the Central Limit Theorem (Exercises)
  65. 7.5: Central Limit Theorem - Pocket Change (Worksheet)
  66. 7.6: Central Limit Theorem - Cookie Recipes (Worksheet)
  67. 7.7: The Central Limit Theorem (Exercises)
  68. 08: Confidence Intervals
  69. 8.1: Prelude to Confidence Intervals
  70. 8.2: A Single Population Mean using the Normal Distribution
  71. A Single Population Mean using the Normal Distribution (Exercises)
  72. 8.3: A Single Population Mean using the Student t-Distribution
  73. 8.4: A Population Proportion
  74. 8.5: Confidence Interval - Home Costs (Worksheet)
  75. 8.6: Confidence Interval -Place of Birth (Worksheet)
  76. 8.7: Confidence Interval -Women's Heights (Worksheet)
  77. 8.8: Confidence Intervals (Exercises)
  78. 8.9: Confidence Intervals (Summary)
  79. 09: Hypothesis Testing with One Sample
  80. 9.1: Prelude to Hypothesis Testing
  81. 9.2: Null and Alternative Hypotheses
  82. Null and Alternative Hypotheses (Exercises)
  83. 9.3: Outcomes and the Type I and Type II Errors
  84. Outcomes and the Type I and Type II Errors (Exercises)
  85. 9.4: Distribution Needed for Hypothesis Testing
  86. Distribution Needed for Hypothesis Testing (Exercises)
  87. 9.5: Rare Events, the Sample, Decision and Conclusion
  88. Rare Events, the Sample, Decision and Conclusion (Exercises)
  89. 9.6: Additional Information and Full Hypothesis Test Examples
  90. 9.7: Hypothesis Testing of a Single Mean and Single Proportion (Worksheet)
  91. 9.8: Hypothesis Testing with One Sample (Exercises)
  92. 10: Hypothesis Testing with Two Samples
  93. 10.1: Prelude to Hypothesis Testing with Two Samples
  94. 10.2: Two Population Means with Unknown Standard Deviations
  95. 10.3: Two Population Means with Known Standard Deviations
  96. 10.4: Comparing Two Independent Population Proportions
  97. 10.5: Matched or Paired Samples
  98. 10.6: Hypothesis Testing for Two Means and Two Proportions (Worksheet)
  99. 10.7: Hypothesis Testing with Two Samples (Exercises)
  100. 11: The Chi-Square Distribution
  101. 11.01: Prelude to The Chi-Square Distribution
  102. 11.02: Facts About the Chi-Square Distribution
  103. 11.03: Goodness-of-Fit Test
  104. 11.04: Test of Independence
  105. 11.05: Test for Homogeneity
  106. 11.06: Comparison of the Chi-Square Tests
  107. 11.07: Test of a Single Variance
  108. 11.08: Lab 1: Chi-Square Goodness-of-Fit (Worksheet)
  109. 11.09: Lab 2: Chi-Square Test of Independence (Worksheet)
  110. 11.10: The Chi-Square Distribution (Exercises)
  111. 12: Linear Regression and Correlation
  112. 12.01: Prelude to Linear Regression and Correlation
  113. 12.02: Linear Equations
  114. Linear Equations (Exercises)
  115. 12.03: Scatter Plots
  116. Scatter Plots (Exercises)
  117. 12.04: The Regression Equation
  118. The Regression Equation (Exercise)
  119. 12.05: Testing the Significance of the Correlation Coefficient
  120. Testing the Significance of the Correlation Coefficient (Exercises)
  121. 12.06: Prediction
  122. Prediction (Exercises)
  123. 12.07: Outliers
  124. Outliers (Exercises)
  125. 12.08: Regression - Distance from School (Worksheet)
  126. 12.09: Regression - Textbook Cost (Worksheet)
  127. 12.10: Regression - Fuel Efficiency (Worksheet)
  128. 12.11: Linear Regression and Correlation (Exercises)
  129. 13: F Distribution and One-Way ANOVA
  130. 13.1: Prelude to F Distribution and One-Way ANOVA
  131. 13.2: One-Way ANOVA
  132. 13.3: The F Distribution and the F-Ratio
  133. 13.4: Facts About the F Distribution
  134. 13.5: Test of Two Variances
  135. 13.6: Lab: One-Way ANOVA
  136. 13.7: F Distribution and One-Way ANOVA (Exercises)
  137. 14: Back Matter
  138. 15: Front Matter
  139. 15.1: TitlePage
  140. 15.2: InfoPage
  141. 15.3: Table of Contents