In this assignment, you will be required to use the Heart Rate Dataset to complete the following: Identify the variables in
Instructions
In this assignment, you will be required to use the Heart Rate Dataset to complete the following:
- Identify the variables in the dataset
- Classify each variable as qualitative or quantitative discrete or quantitative continuous
- Specify the possible values of each variable
- Give a brief written description of what each variable tells us about the data provided.
Steps
- Open the Heart Rate Dataset in Excel
- There are 3 columns of data. Each column represents a different variable. What are the 3 variables represented in the dataset?
- Identify each of the 3 variables as qualitative, quantitative discrete, or quantitative continuous
- Identify the possible values of each of the 3 variables in this dataset.
- Briefly describe what information each of the 3 variables tells us about the data
Additional Instructions:
Your assignment should be typed into a Word or other word processing document, formatted in APA style. The assignments must include
- Running head
- A title page with
- Assignment name
- Your name
- Professor’s name
- Course
Heart rate
| Heart rate before and after exercise | |||
| M=0 F=1 | Resting | After Exercise | |
| 0 | 55.0 | 65.0 | |
| 0 | 67.7 | 79.4 | |
| 0 | 80.3 | 93.4 | |
| 0 | 85.2 | 97.7 | |
| 0 | 86.3 | 99.7 | |
| 0 | 76.6 | 83.7 | |
| 0 | 94.4 | 101.9 | |
| 0 | 86.4 | 100.6 | |
| 0 | 83.4 | 97.4 | |
| 0 | 89.8 | 97.4 | |
| 0 | 88.7 | 97.1 | |
| 0 | 78.4 | 87.2 | |
| 0 | 67.0 | 79.9 | |
| 0 | 85.0 | 100.0 | |
| 0 | 86.2 | 95.9 | |
| 0 | 83.9 | 93.9 | |
| 0 | 78.1 | 87.2 | |
| 0 | 64.0 | 70.7 | |
| 0 | 72.8 | 86.7 | |
| 0 | 65.0 | 75.0 | |
| 0 | 80.2 | 83.3 | |
| 0 | 78.2 | 86.0 | |
| 0 | 62.0 | 88.0 | |
| 0 | 75.5 | 84.4 | |
| 0 | 82.7 | 89.1 | |
| 0 | 87.7 | 95.1 | |
| 0 | 76.0 | 88.7 | |
| 0 | 73.4 | 82.7 | |
| 0 | 80.1 | 94.6 | |
| 0 | 77.6 | 84.6 | |
| 0 | 76.6 | 86.4 | |
| 0 | 85.6 | 96.2 | |
| 0 | 74.2 | 82.1 | |
| 0 | 79.0 | 91.6 | |
| 0 | 74.6 | 86.7 | |
| 0 | 88.8 | 98.8 | |
| 0 | 82.1 | 85.6 | |
| 0 | 77.6 | 80.6 | |
| 0 | 77.9 | 83.8 | |
| 0 | 72.0 | 93.9 | |
| 0 | 81.6 | 90.3 | |
| 0 | 91.2 | 100.6 | |
| 0 | 80.3 | 88.0 | |
| 0 | 76.7 | 91.8 | |
| 0 | 88.4 | 103.0 | |
| 0 | 75.2 | 86.5 | |
| 0 | 75.2 | 84.9 | |
| 0 | 73.1 | 71.9 | |
| 0 | 77.0 | 84.7 | |
| 0 | 59.0 | 68.2 | |
| 0 | 84.9 | 96.0 | |
| 0 | 87.5 | 105.9 | |
| 0 | 75.6 | 84.3 | |
| 0 | 84.0 | 90.4 | |
| 0 | 78.2 | 94.0 | |
| 0 | 86.6 | 90.6 | |
| 0 | 84.9 | 95.1 | |
| 0 | 78.8 | 90.4 | |
| 0 | 69.4 | 82.6 | |
| 0 | 78.3 | 91.1 | |
| 0 | 76.9 | 92.3 | |
| 0 | 84.2 | 87.9 | |
| 0 | 76.3 | 85.9 | |
| 0 | 86.3 | 99.7 | |
| 0 | 72.3 | 80.9 | |
| 0 | 81.8 | 93.8 | |
| 0 | 92.8 | 99.8 | |
| 0 | 74.8 | 90.2 | |
| 0 | 91.7 | 99.2 | |
| 0 | 71.0 | 87.0 | |
| 0 | 96.1 | 100.2 | |
| 0 | 82.5 | 95.1 | |
| 0 | 81.9 | 97.5 | |
| 0 | 89.7 | 94.8 | |
| 0 | 81.4 | 100.9 | |
| 0 | 74.8 | 94.0 | |
| 0 | 88.1 | 102.1 | |
| 0 | 69.2 | 81.4 | |
| 0 | 78.8 | 90.9 | |
| 0 | 85.3 | 94.2 | |
| 0 | 74.8 | 81.3 | |
| 0 | 77.7 | 89.9 | |
| 0 | 78.0 | 89.8 | |
| 0 | 80.5 | 95.3 | |
| 0 | 75.4 | 84.8 | |
| 0 | 81.5 | 84.2 | |
| 0 | 73.9 | 85.2 | |
| 0 | 69.4 | 74.1 | |
| 0 | 89.4 | 96.7 | |
| 0 | 70.9 | 82.0 | |
| 0 | 82.9 | 90.2 | |
| 0 | 60.1 | 79.0 | |
| 0 | 74.5 | 75.6 | |
| 0 | 92.3 | 102.2 | |
| 0 | 87.7 | 98.0 | |
| 0 | 78.9 | 89.7 | |
| 0 | 79.8 | 81.5 | |
| 0 | 85.5 | 97.4 | |
| 0 | 87.3 | 94.1 | |
| 0 | 77.8 | 97.8 | |
| 0 | 71.0 | 80.1 | |
| 0 | 70.0 | 90.7 | |
| 0 | 74.8 | 83.7 | |
| 1 | 69.2 | 79.4 | |
| 1 | 80.5 | 87.4 | |
| 1 | 89.4 | 99.2 | |
| 1 | 74.5 | 88.0 | |
| 1 | 70.0 | 100.0 | |
| 1 | 60.0 | 78.1 | |
| 1 | 79.2 | 90.4 | |
| 1 | 80.5 | 101.3 | |
| 1 | 75.4 | 93.1 | |
| 1 | 83.7 | 90.5 | |
| 1 | 73.9 | 89.1 | |
| 1 | 76.0 | 90.8 | |
| 1 | 85.2 | 93.5 | |
| 1 | 82.1 | 93.5 | |
| 1 | 76.3 | 87.0 | |
| 1 | 97.0 | 104.5 | |
| 1 | 81.5 | 86.5 | |
| 1 | 65.3 | 86.3 | |
| 1 | 60.8 | 86.7 | |
| 1 | 78.5 | 89.9 | |
| 1 | 60.4 | 97.6 | |
| 1 | 89.8 | 92.9 | |
| 1 | 87.8 | 98.5 | |
| 1 | 76.2 | 89.9 | |
| 1 | 74.2 | 88.8 | |
| 1 | 67.4 | 78.8 | |
| 1 | 75.5 | 80.2 | |
| 1 | 80.0 | 90.2 | |
| 1 | 76.4 | 88.0 | |
| 1 | 60.0 | 95.7 | |
| 1 | 89.2 | 96.9 | |
| 1 | 83.3 | 87.7 | |
| 1 | 85.8 | 90.4 | |
| 1 | 75.3 | 84.1 | |
| 1 | 77.9 | 99.0 | |
| 1 | 70.0 | 83.0 | |
| 1 | 88.0 | 94.2 | |
| 1 | 86.9 | 95.0 | |
| 1 | 87.1 | 95.9 | |
| 1 | 60.3 | 82.7 | |
| 1 | 81.2 | 90.7 | |
| 1 | 82.9 | 91.9 | |
| 1 | 87.4 | 103.6 | |
| 1 | 83.0 | 90.0 | |
| 1 | 76.8 | 83.3 | |
| 1 | 76.9 | 87.7 | |
| 1 | 79.8 | 88.2 | |
| 1 | 83.2 | 93.0 | |
| 1 | 79.5 | 88.6 | |
| 1 | 82.4 | 89.3 | |
| 1 | 80.8 | 84.2 | |
| 1 | 83.2 | 94.5 | |
| 1 | 71.6 | 81.5 | |
| 1 | 82.8 | 93.1 | |
| 1 | 76.8 | 92.8 | |
| 1 | 93.2 | 89.4 | |
| 1 | 91.4 | 100.9 | |
| 1 | 97.3 | 103.3 | |
| 1 | 88.3 | 90.1 | |
| 1 | 80.6 | 85.2 | |
| 1 | 87.4 | 91.7 | |
| 1 | 96.5 | 99.3 | |
| 1 | 77.9 | 91.6 | |
| 1 | 76.1 | 84.1 | |
| 1 | 85.2 | 89.7 | |
| 1 | 68.6 | 72.8 | |
| 1 | 79.4 | 91.0 | |
| 1 | 85.2 | 99.1 | |
| 1 | 74.3 | 85.6 | |
| 1 | 74.3 | 89.2 | |
| 1 | 78.5 | 98.5 | |
| 1 | 80.4 | 90.8 | |
| 1 | 82.9 | 85.9 | |
| 1 | 78.9 | 90.7 | |
| 1 | 78.6 | 87.0 | |
| 1 | 87.5 | 93.9 | |
| 1 | 78.9 | 91.4 | |
| 1 | 80.0 | 89.1 | |
| 1 | 80.4 | 89.2 | |
| 1 | 88.3 | 90.5 | |
| 1 | 80.6 | 95.9 | |
| 1 | 85.8 | 90.5 | |
| 1 | 84.6 | 93.0 | |
| 1 | 90.5 | 101.2 | |
| 1 | 92.4 | 101.2 | |
| 1 | 84.4 | 96.7 | |
| 1 | 82.3 | 86.9 | |
| 1 | 77.2 | 85.8 | |
| 1 | 83.3 | 82.1 | |
| 1 | 86.2 | 98.9 | |
| 1 | 81.3 | 97.7 | |
| 1 | 90.2 | 96.4 | |
| 1 | 78.4 | 85.5 | |
| 1 | 84.7 | 90.9 | |
| 1 | 89.7 | 94.3 | |
| 1 | 78.4 | 88.0 | |
| 1 | 70.0 | 80.0 | |
,
Introductory Statistics
OpenStax College Rice University 6100 Main Street MS-375 Houston, Texas 77005
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Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 1: Sampling and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1 Definitions of Statistics, Probability, and Key Terms . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Data, Sampling, and Variation in Data and Sampling . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Frequency, Frequency Tables, and Levels of Measurement . . . . . . . . . . . . . . . . . . 26 1.4 Experimental Design and Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.5 Data Collection Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1.6 Sampling Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Chapter 2: Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs . . . . . . . . . . . . . . 66 2.2 Histograms, Frequency Polygons, and Time Series Graphs . . . . . . . . . . . . . . . . . . 75 2.3 Measures of the Location of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.4 Box Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 2.5 Measures of the Center of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 2.6 Skewness and the Mean, Median, and Mode . . . . . . . . . . . . . . . . . . . . . . . . . 105 2.7 Measures of the Spread of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 2.8 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Chapter 3: Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 3.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 3.2 Independent and Mutually Exclusive Events . . . . . . . . . . . . . . . . . . . . . . . . . . 170 3.3 Two Basic Rules of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 3.4 Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 3.5 Tree and Venn Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 3.6 Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Chapter 4: Discrete Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 4.1 Probability Distribution Function (PDF) for a Discrete Random Variable . . . . . . . . . . . 228 4.2 Mean or Expected Value and Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . 230 4.3 Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 4.4 Geometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 4.5 Hypergeometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 4.6 Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 4.7 Discrete Distribution (Playing Card Experiment) . . . . . . . . . . . . . . . . . . . . . . . . 255 4.8 Discrete Distribution (Lucky Dice Experiment) . . . . . . . . . . . . . . . . . . . . . . . . . 258
Chapter 5: Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 5.1 Continuous Probability Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 5.2 The Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 5.3 The Exponential Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 5.4 Continuous Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
Chapter 6: The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 6.1 The Standard Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 6.2 Using the Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 6.3 Normal Distribution (Lap Times) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 6.4 Normal Distribution (Pinkie Length) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
Chapter 7: The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 7.1 The Central Limit Theorem for Sample Means (Averages) . . . . . . . . . . . . . . . . . . 374 7.2 The Central Limit Theorem for Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 7.3 Using the Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 7.4 Central Limit Theorem (Pocket Change) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 7.5 Central Limit Theorem (Cookie Recipes) . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
Chapter 8: Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 8.1 A Single Population Mean using the Normal Distribution . . . . . . . . . . . . . . . . . . . 417 8.2 A Single Population Mean using the Student t Distribution . . . . . . . . . . . . . . . . . . 427 8.3 A Population Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 8.4 Confidence Interval (Home Costs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 8.5 Confidence Interval (Place of Birth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 8.6 Confidence Interval (Women's Heights) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
Chapter 9: Hypothesis Testing with One Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 9.1 Null and Alternative Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 9.2 Outcomes and the Type I and Type II Errors . . . . . . . . . . . . . . . . . . . . . . . . . . 476 9.3 Distribution Needed for Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 478 9.4 Rare Events, the Sample, Decision and Conclusion . . . . . . . . . . . . . . . . . . . . . . 479
9.5 Additional Information and Full Hypothesis Test Examples . . . . . . . . . . . . . . . . . . 482 9.6 Hypothesis Testing of a Single Mean and Single Proportion . . . . . . . . . . . . . . . . . . 498
Chapter 10: Hypothesis Testing with Two Samples . . . . . . . . . . . . . . . . . . . . . . . . . 529 10.1 Two Population Means with Unknown Standard Deviations . . . . . . . . . . . . . . . . . 530 10.2 Two Population Means with Known Standard Deviations . . . . . . . . . . . . . . . . . . 538 10.3 Comparing Two Independent Population Proportions . . . . . . . . . . . . . . . . . . . . 541 10.4 Matched or Paired Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 10.5 Hypothesis Testing for Two Means and Two Proportions . . . . . . . . . . . . . . . . . . . 551
Chapter 11: The Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 11.1 Facts About the Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 582 11.2 Goodness-of-Fit Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 11.3 Test of Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592 11.4 Test for Homogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596 11.5 Comparison of the Chi-Square Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 11.6 Test of a Single Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600 11.7 Lab 1: Chi-Square Goodness-of-Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602 11.8 Lab 2: Chi-Square Test of Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
Chapter 12: Linear Regression and Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . 637 12.1 Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638 12.2 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640 12.3 The Regression Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 12.4 Testing the Significance of the Correlation Coefficient . . . . . . . . . . . . . . . . . . . . 649 12.5 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654 12.6 Outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655 12.7 Regression (Distance from School) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663 12.8 Regression (Textbook Cost) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 12.9 Regression (Fuel Efficiency) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667
Chapter 13: F Distribution and One-Way ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 13.1 One-Way ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700 13.2 The F Distribution and the F-Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701 13.3 Facts About the F Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 13.4 Test of Two Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 13.5 Lab: One-Way ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715
Appendix A: Review Exercises (Ch 3-13) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739 Appendix B: Practice Tests (1-4) and Final Exams . . . . . . . . . . . . . . . . . . . . . . . . . . 765 Appendix C: Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819 Appendix D: Group and Partner Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823 Appendix E: Solution Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829 Appendix F: Mathematical Phrases, Symbols, and Formulas . . . . . . . . . . . . . . . . . . . . 833 Appendix G: Notes for the TI-83, 83+, 84, 84+ Calculators . . . . . . . . . . . . . .
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