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A G.U.E.S.T. course in statistics Bob Guest Distinguished Lecturer University of Tennessee Mathematics Department [email protected] (those are zeros) A G.U.E.S.T course in statistics is: Guided Understanding by Experiencing Statistics Together This Course is Under Construction Math 115 Statistical Reasoning A non calculus based general education introductory statistics course The Idea • Student focused active learning course (more than 50% of class time) • Some instructor led discovery sprinkled in • Strategic portions of the course flipped Why Portable Populations? Course objective #4) Using the relationship between samples and the populations they are taken from in combination with the fact that when samples are truly random they are also predictable to calculate and apply sampling distributions to various real world situations. By having the students experiencing the examples instead of just reading them, they are developing a sense of intuition about the subject as well as formulating their own questions in real time as we carry out the experiment. This allows them to connect their thoughts and understanding to their experience rather than having to contemplate abstract situations in their mind. This results in a deeper understanding of the concepts allowing students to learn to solve problems rather than simply memorize routines for coming up with solutions to problems. Examples of Portable Populations • 5000 random Scrabble tiles Used to create customized populations • 25 decks of Uno Cards Used to create customized populations • “Monopoly” and “Vegas” dice Why use these? Scrabble tiles and Uno cards • Durable • Light Weight • Quantitative data and Categorical data Why use these? “Monopoly” and “Vegas” dice • Durable • Light Weight • Quantitative data and Categorical data • Challenge assumptions of fairness Examples of Populations Blue Green Yellow Red Mega Deck #0 2 4 0 3 #1 3 8 8 3 #2 5 8 8 3 #3 7 3 8 3 #4 8 1 8 4 #5 8 1 8 4 #6 7 3 0 8 #7 5 6 0 8 #8 3 8 0 8 #9 2 8 0 6 TOTALS 50 50 40 50 9 22 24 21 21 21 18 19 19 16 190 Symmetric Bimodal Uniform Skewed left Examples of Activities Basic probability using the “mega deck” If ONE card is randomly selected from a newly shuffled deck find these probabilities: A) It is a 4? B) It is a 5 given it is blue? C) It is red and is a 7? D) If one card is chosen and you see that it is a yellow card, what is the probability that the card is a 9? E) It is a 6 or is green? F) If Four different cards are dealt at random without replacement, what is the probability that they are all yellow? G) If 150 different cards are dealt at random without replacement, what is the probability that there will be at least one blue card dealt? Examples of Activities Using the Blue (symmetric), Green (Bimodal), Yellow (Uniform) and Red (Skewed left) decks. Calculate the discrete population mean, variance and standard deviation for each color and graph each population Examples of Activities Using the Blue (symmetric), Green (Bimodal), Yellow (Uniform) and Red (Skewed left) decks. Transform ( x c and cx ) these populations to find the impact on the mean, variance, standard deviation and distribution leading to… x having a mean of 0 and standard deviation of 1 Examples of Activities Another set of exercises leads students to discover: 2 2 X X and X n n so... X X X X n has a mean of 0 and standard deviation of 1 Examples of Activities Using the Blue (symmetric), Green (Bimodal), Yellow (Uniform) and Red (Skewed left) decks. Each student collects a sample of size n = 10, 25 and 50 from each deck (used multiple times in the semester) Basic sample statistics calculated, then later confidence intervals are calculated and hypothesis tests are done. Examples of Activities The results from all students are consolidated and used to demonstrate: 1) The random nature of sample statistics 2) Sampling distributions 3) Compare statistical results to KNOWN population parameters. Semester project There is a large population of Scrabble tiles and one of Uno cards 1) The students collect data from these populations 2) They use the tools they have developed to draw conclusions about these UNKNOWN populations.