spr24-exam-01-snowfall

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University of Minnesota-Twin Cities *

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3264

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Statistics

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Apr 3, 2024

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docx

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Uploaded by SuperHumanSnakePerson1279

EPsy 3264: Basic and Applied Statistics Exam #1 12 pts. Average snowfall In the Introduction to Monte Carlo Simulation course activity, you used a model of a population to randomly generate outcomes for a sample of data. The sample of data was then summarized using a mean, count, proportion, etc. This process was then repeated a number of times and the distribution of the sample’s summaries was then examined to study the variation that would be expected based on the data generating process (DGP). This assignment will give you more practice with using Monte Carlo simulation to study the variation in sample summaries. Modeling average snowfall One real-life situation that can be modeled as a random process is the number of days it snows in Minnesota, specifically in Minneapolis. As with most real-life situations, it can be hard to envision this as a random process—and in fact not all properties of weather are random. For example, snowfall patterns can be affected by weather systems and climate change. Warming of the planet causes more moisture in the atmosphere and can lead to higher snowfall amounts and more snowy days. 1 In a typical year in Minneapolis, 365 days, about 10.2% of the days in Minneapolis are snowy. In other words, of the 365 days during the year, the typical snowy days was 10.2%, and 89.8% of those days did not have snowfall. ● Use TinkerPlots™ to set up a sampler based on a typical Minneapolis year, 365 days, and has a snowfall percentage of 10.2%. Explore the Observed Data All questions worth 1 point unless otherwise indicated. 1. Copy and paste (or sketch) a picture of your TinkerPlot sampler into your word-processed document. Explain why you chose the sampling device and the values (repeat, percentages, draw, etc) you used to create it. (2pts) 2. Run the sampler to generate the outcomes for 365 days. Plot the outcomes for this hypothetical year. Also compute the number (count) of snow and no snow for this year. Copy and paste (or sketch) this plot into your word-processed document.

EPsy 3264: Basic and Applied Statistics Exam #1 12 pts. Carry Out Multiple Trials of the Simulation 3. Using the automation feature, run 50 trials of your simulation. Copy and paste the plot of the results from your 50 trials into your word-processed document. 4. Using the context of snowfall, what does a dot in this plot represent? 5. Give and interpret the mean value for your 50 results in context. (2pts) 6. By referring to the model you set up in your TinkerPlots sampler, explain how you could have predicted what the value of the mean would be before looking at the plot. 7. Based on the plot of the 50 results, describe the variation in the number of days of snow by giving the endpoints of the range where most counts lie in the plot 8. Use the Divider tool in TinkerPlots to find the percent of the 50 results that fall in the range you provided in Question #7. Report the results. 9. In 2010, there were 51 days with measurable snow in Minneapolis or 13.97.% of 2010. Is this daily amount of snowfall likely based on the range you gave in Question #7? 10. Based on your answer to Question #9, is a year with 13.97% or 51 snowy days “extraordinary” by Minneapolis standards? Explain by referencing your simulation results. Copy and paste the plot of results (with the divider from #8 and add a reference line) into your word-processed document.

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