The activity is designed to help students develop a better intuitive understanding …
The activity is designed to help students develop a better intuitive understanding of what is meant by variability in statistics. Emphasis is placed on the standard deviation as a measure of variability. As they learn about the standard deviation, many students focus on the variability of bar heights in a histogram when asked to compare the variability of two distributions. For these students, variability refers to the variation in bar heights. Other students may focus only on the range of values, or the number of bars in a histogram, and conclude that two distributions are identical in variability even when it is clearly not the case. This activity can help students discover that the standard deviation is a measure of the density of values about the mean of a distribution and to become more aware of how clusters, gaps, and extreme values affect the standard deviation.
The Food and Drug Administration requires pharmaceutical companies to establish a shelf …
The Food and Drug Administration requires pharmaceutical companies to establish a shelf life for all new drug products through a stability analysis. This is done to ensure the quality of the drug taken by an individual is within established levels. The purpose of this out-of-class project or in-class example is to determine the shelf life of a new drug. This is done through using simple linear regression models and correctly interpreting confidence and prediction intervals. An Excel spreadsheet and SAS program are given to help perform the analysis.
This article describes an interactive activity illustrating general properties of hypothesis testing …
This article describes an interactive activity illustrating general properties of hypothesis testing and hypothesis tests for proportions. Students generate, collect, and analyze data. Through simulation, students explore hypothesis testing concepts. Concepts illustrated are: interpretation of p-values, type I error rate, type II error rate, power, and the relationship between type I and type II error rates and power. This activity is appropriate for use in an introductory college or high school statistics course.
This group activity focuses on conducting an experiment to determine which of …
This group activity focuses on conducting an experiment to determine which of two brands of paper towels are more absorbent by measuring the amount of water absorbed. A two-sample t-test can be used to analyze the data, or simple graphics and descriptive statistics can be used as an exploratory analysis. Students are asked to think about design issues, and to write a short report stating their results and conclusions, along with an evaluation of the experimental design.
Christopher J. Malone, Christopher R. Bilder, Deborah J. Rumsey, John E. Boyer, Kansas State University, Ohio State University, Oklahoma State University
This activity is part of the community collection of teaching materials on …
This activity is part of the community collection of teaching materials on climate and energy topics. These materials were submitted by faculty as part of the CLEAN Energy Workshop, held in April, 2011.
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Students are introduced to the technology of flexible circuits, some applications and …
Students are introduced to the technology of flexible circuits, some applications and the photolithography fabrication process. They are challenged to determine if the fabrication process results in a change in the circuit dimensions since, as circuits get smaller and smaller (nano-circuits), this could become very problematic. The lesson prepares students to conduct the associated activity in which they perform statistical analysis (using Excel® and GeoGebra) to determine if the circuit dimension sizes before and after fabrication are in fact statistically different. A PowerPoint® presentation and post-quiz are provided. This lesson and its associated activity are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.
Students apply pre-requisite statistics knowledge and concepts learned in an associated lesson …
Students apply pre-requisite statistics knowledge and concepts learned in an associated lesson to a real-world state-of-the-art research problem that asks them to quantitatively analyze the effectiveness of different cracked steel repair methods. As if they are civil engineers, students statistically analyze and compare 12 sets of experimental data from seven research centers around the world using measurements of central tendency, five-number summaries, box-and-whisker plots and bar graphs. The data consists of the results from carbon-fiber-reinforced polymer patched and unpatched cracked steel specimens tested under the same stress conditions. Based on their findings, students determine the most effective cracked steel repair method, create a report, and present their results, conclusions and recommended methods to the class as if they were presenting to the mayor and city council. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.
Working as if they are engineers aiming to analyze and then improve …
Working as if they are engineers aiming to analyze and then improve data collection devices for precision agriculture, students determine how accurate temperature sensors are by comparing them to each other. Teams record soil temperature data during a class period while making changes to the samples to mimic real-world crop conditions—such as the addition of water and heat and the removal of the heat. Groups analyze their collected data by finding the mean, median, mode, and standard deviation. Then, the class combines all the team data points in order to compare data collected from numerous devices and analyze the accuracy of their recording devices by finding the standard deviation of temperature readings at each minute. By averaging the standard deviations of each minute’s temperature reading, students determine the accuracy of their temperature sensors. Students present their findings and conclusions, including making recommendations for temperature sensor improvements.
This is a new approach to an introductory statistical inference textbook, motivated …
This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. It is freely available under the Creative Commons License, and includes a software library in Python for making some of the calculations and visualizations easier.
Help! I’m completely new to coding and I need to learn R …
Help! I’m completely new to coding and I need to learn R and RStudio! What do I do?
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A variable is any characteristics, number, or quantity that can be measured …
A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables. It is called a variable because the value may vary between data units in a population, and may change in value over time. There are different ways variables can be described according to the ways they can be studied, measured, and presented.
The authors of this book adapted homework problems to improve accessibility and …
The authors of this book adapted homework problems to improve accessibility and promote diversity, equity, and inclusion in the introductory statistics course they teach at Fitchburg State University. The problems are showcased in this book, but we have also incorporated them into our existing problem sets on an open-source online homework platform called WeBWorK. The problems can be used as a companion to the OpenStax textbook "Introductory Statistics" by Barbara Illowsky and Susan Dean or any other textbook for a semester-long introductory statistics course. For a fuller experience for you and your students, we encourage you to contact us for help accessing the problem sets on WeBWorK. On that platform, students will engage more fully with the questions, and a slightly different version of the same problem will be generated for each student.
As our society increasingly calls for evidence-based decision making, it is important …
As our society increasingly calls for evidence-based decision making, it is important to consider how and when we can draw valid inferences from data. This module will use four recent research studies to highlight key elements of a statistical investigation.
Statistical thinking is a way of understanding a complex world by describing …
Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge. The foundations of statistical thinking come primarily from mathematics and statistics, but also from computer science, psychology, and other fields of study.
A general statistics course, which includes understanding data, measures of central tendency, …
A general statistics course, which includes understanding data, measures of central tendency, measures of variation, binomial distributions, normal distributions, correlation and regression, probability and sampling distributions, Central Limit Theorem, confidence intervals, estimates of population parameters and hypothesis testing. Interpretation and data analysis are emphasized. PREREQUISITES: A grade of C or better in MAT 100 (Intermediate Algebra) or MAT 120 (Math Modeling for Liberal Arts) and placement above or successful completion of ENG 060 (Preparations for College Reading III). A student needs a thorough knowledge of Algebra, good reading skills and familiarity with the graphing calculator before entering this course.
A general statistics course, which includes understanding data, measures of central tendency, …
A general statistics course, which includes understanding data, measures of central tendency, measures of variation, binomial distributions, normal distributions, correlation and regression, probability and sampling distributions, Central Limit Theorem, confidence intervals, estimates of population parameters and hypothesis testing. Interpretation and data analysis are emphasized.
This resource is a lesson gudie for an approach to probability that …
This resource is a lesson gudie for an approach to probability that is collaborative among students and designed to have students experience probability from their own unique perspectives. Some of the goals of the work are to:understand the different approaches in probabilitydeepen intuitive experience of probability by facing probabilistic misconceptionsconduct probability experimentsBuilt in as a goal is the soft skill of conducting research for refereed articles, going beyond internet searches and subsequent page hits in terms of curating resources that can lead to success in a probability class.
This resource is a lesson gudie for an approach to probability that …
This resource is a lesson gudie for an approach to probability that is collaborative among students and designed to have students experience probability from their own unique perspectives. Some of the goals of the work are to:understand the different approaches in probabilitydeepen intuitive experience of probability by facing probabilistic misconceptionsconduct probability experimentsBuilt in as a goal is the soft skill of conducting research for refereed articles, going beyond internet searches and subsequent page hits in terms of curating resources that can lead to success in a probability class.
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