22.1 data gathering techniques homework answers

Statistics Using

Technology By Kathryn Kozak

Photo taken by Richard Kozak at Dorrigo National Park in NSW, Australia

Creative Commons Attribution Sharealike. This license is considered to be some to be the most open license. It allows reuse, remixing, and distribution (including commercial), but requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license.

2014 Kathryn Kozak ISBN: 978-1-312-18519-7

Statistics Using Technology

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Table of Content: Preface iii

Chapter 1: Statistical Basics 1

Section 1.1: What is Statistics? 1 Section 1.2: Sampling Methods 8 Section 1.3: Experimental Design 14 Section 1.4: How Not to Do Statistics 19 Chapter 2: Graphical Descriptions of Data 25 Section 2.1: Qualitative Data 25 Section 2.2: Quantitative Data 36 Section 2.3: Other Graphical Representations of Data 56 Chapter 3: Numerical Descriptions of Data 71 Section 3.1: Measures of Center 71 Section 3.2: Measures of Spread 83 Section 3.3: Ranking 99 Chapter 4: Probability 111 Section 4.1: Empirical Probability 111 Section 4.2: Theoretical Probability 114 Section 4.3: Conditional Probability 130 Section 4.4: Counting Techniques 142 Chapter 5: Discrete Probability Distributions 147 Section 5.1: Basics of Probability Distributions 147 Section 5.2: Binomial Probability Distribution 156 Section 5.3: Mean and Standard Deviation of Binomial Distribution 169 Chapter 6: Continuous Probability Distributions 175 Section 6.1: Uniform Distribution 175 Section 6.2: Graphs of the Normal Distribution 178 Section 6.3: Finding Probabilities for the Normal Distribution 181 Section 6.4: Assessing Normality 190 Section 6.5: Sampling Distribution and the Central Limit Theorem 202

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Chapter 7: One-Sample Inference 215 Section 7.1: Basics of Hypothesis Testing 215 Section 7.2: One-Sample Proportion Test 228 Section 7.3: One-Sample Test for the Mean 234 Chapter 8: Estimation 247 Section 8.1: Basics of Confidence Intervals 247 Section 8.2: One-Sample Interval for the Proportion 250 Section 8.3: One-Sample Interval for the Mean 255 Chapter 9: Two-Sample Inference 265 Section 9.1: Paired Samples for Two Means 265 Section 9.2: Independent Samples for Two Means 284 Section 9.3: Two Proportions 306 Chapter 10: Regression and Correlation 317 Section 10.1: Regression 317 Section 10.2: Correlation 336 Section 10.3: Inference for Regression and Correlation 344 Chapter 11: Chi-Square and ANOVA Tests 359 Section 11.1: Chi-Square Test for Independence 359 Section 11.2: Chi-Square Goodness of Fit 375 Section 11.3: Analysis of Variance (ANOVA) 382 Appendix: Critical Value Tables 395 Table A.1: Normal Critical Values for Confidence Levels 396 Table A.2: Critical Values for t-Interval 397 Index 398

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Preface: I hope you find this book useful in teaching statistics. When writing this book, I tried to follow the GAISE Standards (GAISE recommendations. (2014, January 05). Retrieved from http://www.amstat.org/education/gaise/GAISECollege_Recommendations.pdf ), which are

1.) Emphasis statistical literacy and develop statistical understanding. 2.) Use real data. 3.) Stress conceptual understanding, rather than mere knowledge of procedure. 4.) Foster active learning in the classroom. 5.) Use technology for developing concepts and analyzing data.

To this end, I ask students to interpret the results of their calculations. I incorporated the use of technology for most calculations. Because of that you will not find me using any of the computational formulas for standard deviations or correlation and regression since I prefer students understand the concept of these quantities. Also, because I utilize technology you will not find the standard normal table, Student’s t-table, binomial table, chi-square distribution table, and F-distribution table in the book. The only tables I provided were for critical values for confidence intervals since they are more difficult to find using technology. Another difference between this book and other statistics books is the order of hypothesis testing and confidence intervals. Most books present confidence intervals first and then hypothesis tests. I find that presenting hypothesis testing first and then confidence intervals is more understandable for students. Lastly, I have de- emphasized the use of the z-test. In fact, I only use it to introduce hypothesis testing, and never utilize it again. You may also notice that when I introduced hypothesis testing and confidence intervals, proportions were introduced before means. However, when two sample tests and confidence intervals are introduced I switched this order. This is because usually many instructors do not discuss the proportions for two samples. However, you might try assigning problems for proportions without discussing it in class. After doing two samples for means, the proportions are similar. Lastly, to aid student understanding and interest, most of the homework and examples utilize real data. Again, I hope you find this book useful for your introductory statistics class. I want to make a comment about the mathematical knowledge that I assumed the students possess. The course for which I wrote this book has a higher prerequisite than most introductory statistics books. However, I do feel that students can read and understand this book as long as they have had basic algebra and can substitute numbers into formulas. I do not show how to create most of the graphs, but most students should have been exposed to them in high school. So I hope the mathematical level is appropriate for your course. The technology that I utilized for creating the graphs was Microsoft Excel, and I utilized the TI-83/84 graphing calculator for most calculations, including hypothesis testing, confidence intervals, and probability distributions. This is because these tools are readily available to my students. Please feel free to use any other technology that is more appropriate for your students. Do make sure that you use some technology.

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Acknowledgments: I would like to thank the following people for taking their valuable time to review the book. Their comments and insights improved this book immensely.

Jane Tanner, Onondaga Community College Rob Farinelli, College of Southern Maryland Carrie Kinnison, retired engineer Sean Simpson, Westchester Community College Kim Sonier, Coconino Community College Jim Ham, Delta College