Qualitative and Quantitative Approaches Word Count: 137942 (Note: This resource's metadata has …
Qualitative and Quantitative Approaches
Word Count: 137942
(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)
In this project students will explore changes in income over time for …
In this project students will explore changes in income over time for the three largest racial/ethnic groups: Whites, Blacks and Hispanics. Students Will: Graph real data income data from different ethnic groups over time.Make decisions about which data set is best for comparison.Graph differences in income between ethnic groups.Compute the differences in income for each of the groupsDraw conclusions about the characteristics of the graphs and the average rate of change.General Education (Quantitative Reasoning)
In this activity, students will determine whether there is a statistically significant …
In this activity, students will determine whether there is a statistically significant difference in the number of watts of power produced on individual solar panels at Bryn Mawr College.
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Sonar technology allowed scientists to produce high-resolution maps of the sea floor …
Sonar technology allowed scientists to produce high-resolution maps of the sea floor for the first time. This sonar demonstration uses a Human Sound Wave to image the "sea floor" in a lecture hall. In doing so, students can see two-way travel times collected and plotted in real time. Students also evaluate sources of error that can be applied to a real sonar device.
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A one-way analysis of variance exercise using data on species diversities from …
A one-way analysis of variance exercise using data on species diversities from vernal pools.Data are from vernal pools in Willowbrook Park (adjacent to College of Staten Island's campus) in spring. The typical ANOVA gives a straightforward result (significant anova, easily-interpreted Tukey-Kramer analysis). This data set requires more nuanced interpretation, as the ANOVA is marginally significant, and Tukey-Kramer yields one significant pairwise comparison between groups. Relative lack of variation within groups explains this apparent enigma.
As if they are engineers, students are tasked to design solar-powered model …
As if they are engineers, students are tasked to design solar-powered model vehicles that are speedy and compact in order to make recommendations to a local car sales company. Teams familiarize themselves with the materials by building solar-panel model car prototypes, following kit instructions, which they test for speed. After making design improvements, they test again. Then they take measurements and calculate the volume of each team’s vehicle. They rank all teams’ vehicles by speed and by size. After data analyses, reflection and team discussion, students write recommendations to the car company about the vehicle they think is best for consumers. Youngsters experience key portions of the engineering design process and learn the importance of testing and collaborating in order to make better products. Pre/post-quizzes and numerous worksheets and handouts are provided.
This collection of spreadsheet-based labs was funded as part of the Digital …
This collection of spreadsheet-based labs was funded as part of the Digital Learning Research Network (dLRN) made possible by a grant from the Bill and Melinda Gates Foundation. The labs were adapted from the Statistics book, “Introduction to Statistics,” published by OpenStax College. The original labs used graphing calculators and were found within the book after each chapter. These interactive spreadsheet-based labs are effective for online and face-face courses. They may also be used with the book (see Resource: Lab Mapping to Book Chapters) or stand-alone.Authors: Barbara Illowsky PhD, Foothill-De Anza Community College District; Larry Green PhD, Lake Tahoe Community College; James Sullivan, Sierra College; Lena Feinman,College of San Mateo; Cindy Moss, Skyline College; Sharon Bober, Pasadena Community College; Lenore Desilets, De Anza Community College.Lab Mapping to Book ChaptersGrading RubricLabsUnivariarate Data Normal DistributionCentral Limit TheoremHyporhesis Test - Single MeanHyporhesis Test - Single ProportionGoodness of FitLinear Regression
Learning about complexities carbon stabilization firsthand with the Princeton University Carbon Mitigation …
Learning about complexities carbon stabilization firsthand with the Princeton University Carbon Mitigation Initiave's Sabilization Wedges Game
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Dawson (1995) presented a data set giving a population at risk and …
Dawson (1995) presented a data set giving a population at risk and fatalities for an “unusual episode” (the sinking of the ocean liner Titanic) and discussed the use of the data set in a first statistics course as an elementary exercise in statistical thinking, the goal being to deduce the origin of the data. Simonoff (1997) discussed the use of this data set in a second statistics course to illustrate logistic regression. Moore (2000) used an abbreviated form of the data set in a chapter exercise on the chi-square test. This article describes an activity that illustrates contingency table (two-way table) analysis. Students use contingency tables to analyze the “unusual episode” data (from Dawson 1995) and attempt to use their analysis to deduce the origin of the data. The activity is appropriate for use in an introductory college statistics course or in a high school AP statistics course.
The activity begins with an explanation of the Caesar Shift for message …
The activity begins with an explanation of the Caesar Shift for message encryption (Singh, 1999). The Caesar Shift is a translation of the alphabet; for example, a five-letter shift would code the letter a as f, b as g, … z as e. We describe a five-step process for decoding an encrypted message. First, groups of size 4 construct a frequency table of the letters in two lines of a coded message. Second, students construct a bar chart for a reference message of the frequency of letters in the English language. Third, students create a bar chart of the coded message. Fourth, students visually compare the bar chart of the reference message (step 2) to the bar chart of the coded message (step 3). Based on this comparison, students hypothesize a shift. Fifth, students apply the shift to the coded message.
Students explore the definition and interpretations of the probability of an event …
Students explore the definition and interpretations of the probability of an event by investigating the long run proportion of times a sum of 8 is obtained when two balanced dice are rolled repeatedly. Making use of hand calculations, computer simulations, and descriptive techniques, students encounter the laws of large numbers in a familiar setting. By working through the exercises, students will gain a deeper understanding of the qualitative and quantitative relationships between theoretical probability and long run relative frequency. Particularly, students investigate the proximity of the relative frequency of an event to its probability and conclude, from data, that the dispersion of the relative frequency diminishes on the order .
This activity provides students with 24 histograms representing distributions with differing shapes …
This activity provides students with 24 histograms representing distributions with differing shapes and characteristics. By sorting the histograms into piles that seem to go together, and by describing those piles, students develop awareness of the different versions of particular shapes (e.g., different types of skewed distributions, or different types of normal distributions), that not all histograms are easy to classify, that there is a difference between models (normal, uniform) and characteristics (skewness, symmetry, etc.).
This activity leads students to appreciate the usefulness of simulations for approximating …
This activity leads students to appreciate the usefulness of simulations for approximating probabilities. It also provides them with experience calculating probabilities based on geometric arguments and using the bivariate normal distribution. We have used it in courses in probability and mathematical statistics, as well as in an introductory statistics course at the post-calculus level.
This article describes an interactive activity illustrating sampling distributions for means, properties …
This article describes an interactive activity illustrating sampling distributions for means, properties of confidence intervals, properties of hypothesis testing, confidence intervals for means, and hypothesis tests for means. Students generate and analyze data and through simulation explore these concepts. The activity is completed in three parts. The three parts of the activity can be used in sequence or they can be used individually as stand alone activities. This allows the educator flexibility in utilizing the activity. Part I illustrates the sampling distribution of the sample mean. Part II illustrates confidence intervals for the population mean. Part III illustrates hypothesis tests for the population mean. This activity is appropriate for use in an introductory college or high school AP statistics course.
As teachers of statistics, we know that residual plots and other diagnostics …
As teachers of statistics, we know that residual plots and other diagnostics are important to deciding whether or not linear regression is appropriate for a set of data. Despite talking with our students about this, many students might believe that if the correlation coefficient is strong enough, these diagnostic checks are not important. The data set included in this activity was created to lure students into a situation that looks on the surface to be appropriate for the use of linear regression but is instead based (loosely) on a quadratic function.
This activity is an advanced version of the “Keep your eyes on …
This activity is an advanced version of the “Keep your eyes on the ball” activity by Bereska, et al. (1999). Students should gain experience with differentiating between independent and dependent variables, using linear regression to describe the relationship between these variables, and drawing inference about the parameters of the population regression line. Each group of students collects data on the rebound heights of a ball dropped multiple times from each of several different heights. By plotting the data, students quickly recognize the linear relationship. After obtaining the least squares estimate of the population regression line, students can set confidence intervals or test hypotheses on the parameters. Predictions of rebound length can be made for new values of the drop height as well. Data from different groups can be used to test for equality of the intercepts and slopes. By focusing on a particular drop height and multiple types of balls, one can also introduce the concept of analysis of variance.
In these activities designed to introduce sampling distributions and the Central Limit …
In these activities designed to introduce sampling distributions and the Central Limit Theorem, students generate several small samples and note patterns in the distributions of the means and proportions that they themselves calculate from these samples.
This group activity illustrates the concepts of size and power of a …
This group activity illustrates the concepts of size and power of a test through simulation. Students simulate binomial data by repeatedly rolling a ten-sided die, and they use their simulated data to estimate the size of a binomial test.
An important objective in hiring is to ensure diversity in the workforce. …
An important objective in hiring is to ensure diversity in the workforce. The race or gender of individuals hired by an organization should reflect the race or gender of the applicant pool. If certain groups are under-represented or over-represented among the employees, then there may be a case for discrimination in hiring. On the other hand, there may be a number of random factors unrelated to discrimination, such as the timing of the interview or competition from other employers, that might cause one group to be over-represented or under-represented. In this exercise, we ask students to investigate the role of randomness in hiring, and to consider how this might be used to help substantiate or refute charges of discrimination.
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