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In this task you will investigate the sampling distribution and model for the proportion of heads that may show up when a coin is tossed repeatedly.
In this task you will investigate the sampling distribution and model for the proportion of heads that may show up when a coin is tossed repeatedly. Toss the coins if you want, but it’s much easier and faster to do a simulation!1.Set up a calculator or computer’s random number generator to simulate tossing a coin 25 times. (One way to do this is to generate 0’s and 1’s you can effectively count the number of heads. Dividing that count by the number of tosses will get you , the sample proportion of heads.)2.Run 20 trials, recording all the sample proportions and make a histogram of the results.3.Repeat your simulation, this time tossing the coin 100 times. Again make a histogram of the 20 sample proportions.4.Compare your two distributions of the proportions of heads observed in your simulations.5.What should have happened? Describe the sampling model for 100 tosses.6.Compare the actual distribution of your twenty sample proportions for 100 tosses to what the sampling model predicts. 7.Describe how your results might differ if you had run 1000 trials for the simulations instead of only 20.Grading:1.Simulations and HistogramsoCompletes 20 trials for eachoConstructs well-labeled graphsoUses the same scale for comparison2.Comparison of HistogramsoCorrectly compares shapes, centers and spreads3.The ModeloChecks conditionsoHas correct parameters4.Comparison of Histogram and ModeloSketches modeloCompares with the histograms from the trialsoDo they match? Why or why not?oWhat would happen if you ran 1000 trials?
