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Math 110, 110S Packet Version 1.0 This Work Is Licensed Under the Creative Commons Attribution-Noncommercial-Sharealike 4.0 Inter- National License Math 110, 110S Packet Version 1.0 This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Inter- national License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/4.0/ or send a let- ter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. Contents 1 Affective Domain 1 Module 1 A Poster Session ..................................... 3 Module 2 Learning Strategies ................................... 7 Module 3 Brainology and Growing Your Brain ......................... 11 Module 3.1 Brainology ..................................... 11 Module 3.2 Grow Your Brain .................................. 17 2 Summarizing Data Graphically and Numerically 21 Module 4 Distributions of Quantitative Data .......................... 23 Module 4.1 Distributions of Quantitative Data: Introduction ............... 23 Module 4.2 Dot Plots ...................................... 27 Module 4.3 Histograms ..................................... 33 Module 4.4 Module 4 Lab ................................... 39 Module 5 Measures of Center ................................... 43 Module 5.1 A Feel for Measures of Center .......................... 43 Module 5.2 The Mean as a Balancing Point ......................... 49 Module 5.3 Shape and Measures of Center ......................... 53 Module 6 Measures of Spread about the Median ........................ 57 Module 6.1 Quantifying Variability Relative to the Median Part 1 ............ 57 Module 6.2 Quantifying Variability Relative to the Median Part 2 ............ 61 Module 6.3 Module 6 Lab ................................... 65 Module 7 Quantifying Variability Relative to the Mean ..................... 67 Module 7.1 Measuring Variability Relative to the Mean: ADM .............. 67 Module 7.2 Using the ADM ................................... 73 Module 7.3 The Standard Deviation ............................. 75 Module 7.4 The Mean and Standard Deviation: Intervals of Typical Measurements . 79 Module 7.5 Module 7 Lab ................................... 83 Module 7.6 Unit 2 Summary Lab ............................... 87 Module 7.7 Unit 2 Project ................................... 89 i 3 Examining Relationships: Quantitative Data 93 Module 8 Scatterplots, Linear Relationships, and Correlation ................ 95 Module 8.1 Introduction to Scatterplots and Association ................. 95 Module 8.2 Direction, Form, and Strength in Scatterplots ................. 99 Module 8.3 Introduction to Linear Correlation: r ...................... 103 Module 8.4 Correlation is not Causation ........................... 105 Module 9 Fitting a Line ....................................... 107 Module 9.1 Introduction to Linear Regression ....................... 107 Module 9.2 Interpreting the Constants ............................ 113 Module 9.3 Lab Assignment .................................. 115 Module 9.4 Unit 3 Project ................................... 117 4 Relationships in Categorical Data with an Introduction to Probability 123 Module 10 Two-Way Tables ..................................... 125 Module 10.1 Relationships between Categorical Data .................... 125 Module 10.2 Introduction to Probabiity and Risk using Two-Way Tables ........ 129 Module 10.3 Lab Assignment .................................. 133 Module 10.4 Unit 4 Project ................................... 135 5 Probability and Probability Distributions 139 Module 11 Probability and Distributions ............................. 141 Module 11.1 Introduction to Probability ........................... 141 Module 11.2 Probability Distributions ............................. 143 Module 12 Continuous Random Variables ............................. 149 Module 12.1 Probability Distributions for Continuous Random Variables ........ 149 Module 12.2 Introduction to the Normal Distribution .................... 155 Module 12.3 Standardizing Scores and the Standard Normal Probability Distribution . 159 Module 12.4 Unit 5 Lab ..................................... 163 6 Types of Statistical Studies and Producing Data 165 Module 13 Producing Data for a Statistical Study ........................ 167 Module 14 Collecting Data—Sampling ............................... 173 Module 14.1 Observational Studies and Sampling ...................... 173 Module 14.2 Random Sampling Demonstration (Optional) ................. 175 Module 15 Collecting Data—Conducting an Experiment .................... 181 Module 15.1 Experiments and Random Assignment .................... 181 Module 15.2 Lab Assignment: Practice with Confounding Variables and Design .... 185 Module 15.3 Unit 6 Project ................................... 187 ii 7 Linking Probability to Statistical Inference 189 Module 16 Introduction to Inference ................................ 191 Module 17 Distribution of Sample Proportions .......................... 193 Module 17.1 Understanding Sampling Variability: Intro. to Sampling Distributions .. 193 Module 17.2 Sampling Distribution for a Population Proportion ............. 197 Module 17.3 Effect of Sample Size on the Sampling Distribution ............. 203 Module 17.4 Mathematical Model for the Distribution of Sample Proportions ..... 207 Module 18 Introduction to Statistical Inference ......................... 213 Module 18.1 Introduction to Conidence Intervals ...................... 213 Module 18.2 Finding a 95% Conidence Interval ....................... 217 Module 18.3 What Does “95% Conident” Really Mean? .................. 221 Module 18.4 Introduction to a Hypothesis Test ....................... 225 Module 18.5 Unit 7 Lab ..................................... 231 8 Inference for One Proportion 237 Module 19 Estimating a Population Proportion ......................... 239 Module 20 Hypothesis Testing ................................... 245 Module 20.1 Hypothesis Testing ................................ 245 Module 20.2 Type I and Type II Errors ............................ 253 Module 20.3 P-Values and What They Mean ......................... 255 Module 21 Hypothesis Test for a Population Proportion .................... 259 Module 21.1 Hypothesis Testing for a Population Proportion ............... 259 Module 21.2 Cautionary Notes about Drawing Conclusions from a Hypothesis Test .. 265 Module 21.3 Unit 8 Lab ..................................... 273 Module 21.4 Unit 8 Project ................................... 275 9 Inference for Means 281 Module 22 Distribution of Sample Means ............................. 283 Module 22.1 Introduction to the Distribution of Sample Means .............. 283 Module 22.2 Modeling the Distribution of Sample Means ................. 291 Module 23 Estimating a Population Mean ............................. 297 Module 23.1 Introduction to the Conidence Interval for Estimating a Population Mean 297 Module 23.2 Adjustments to the Conidence Interval for Estimating a Population Mean 301 Module 24 Hypothesis Test for a Population Mean ........................ 307 Module 24.1 Hypothesis Test for a Population Mean .................... 307 Module 24.2 Hypothesis Test for a Mean with Matched Pairs ............... 313 Module 25 Inference for a Difference between Population Means ............... 319 Module 25.1 Inference for a Difference in Population Means ................ 319 Module 25.2 Unit 9 Lab ..................................... 325 Module 25.3 Unit 9 Project ................................... 331 iii 10 ANOVA 333 Module 26 ANOVA .......................................... 335 11 Chi-Square 343 Module 27 Chi-Square ........................................ 345 Module 27.1 Chi-Square Test for Independence ....................... 345 Module 27.2 Unit 11 Lab ..................................... 353 Module 27.3 Unit 11 Project ................................... 355 12 Vocabulary 357 Module 28 Vocabulary ........................................ 359 iv UNIT 1 Affective Domain Contents Module 1 A Poster Session .................................. 3 Module 2 Learning Strategies ................................ 7 Module 3 Brainology and Growing Your Brain ...................... 11 Module 3.1 Brainology .................................... 11 Module 3.2 Grow Your Brain ................................. 17 1 UNIT 1. AFFECTIVE DOMAIN 2 MODULE 1. A POSTER SESSION Module 1 A Poster Session Breakfast!Cereals!and!Children’s!Health! ! Part!I:!Your!instructor!will!show!you!a!series!of!commercials!for!breakfast!cereals.! After!viewing!and!discussing!these!commercials!as!a!class,!discuss!the!following!four! questions!in!your!group.!Make!notes!of!key!points!raised!in!your!group!to!prepare! for!the!class!discussion.! ! 1) Should!we!be!concerned!about!advertisers!targeting!children!in!breakfast!cereal! advertisements?!Why!or!why!not?! ! ! ! ! ! ! ! ! 2) What!impact,!if!any,!do!you!think!this!advertising!has!on!children’s!health?!Be! specific.! ! ! ! ! ! ! ! 3) How!do!you!define!“unhealthy”!cereals?! ! ! ! ! ! ! ! ! ! ! 4) Do!you!think!this!is!a!world!health!issue!or!one!confined!to!the!United!States?! Explain.! !! ! ! ! ! 3 ! ! UNIT 1. AFFECTIVE DOMAIN Part!II:!For!this!activity!your!group!will!be!working!with!a!data!set!containing! information!about!24!breakfast!cereals.!! ! Question!to!be!investigated:! Are cereals marketed to children less healthy than cereals marketed to adults? ! Instructions:!Answer!this!question!and!back!up!your!answer!with!observations!from! the!data.!! ! Think!It!Through:!! ! • As!a!group,!decide!which!parts!of!the!data!set!you!plan!to!use.!You!do!not!need! to!explore!all!of!the!variables;!choose!one!or!a!few.!!
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