Sampling Distribution Simulation Sarnlng Variabilm is the variability seen In a statistic when repeated sampling is performed. Under certain conditions the sampling variability Mil exhibit a pattern; we can use these patterns to help us use the statistic to estimate the parameter. When the sampling variability exhibits a pattern, we can say it is understandable. We can visualize the sampling variability by plotting the statistics taken from many random samples. This plot is called a sampling distribution. One of the conditions needed to construct a sampling distribution is random sampling. When working with certain statistics we know that the sampling distribution will be bell shaped and peak above the parameter. Today we will use a web applet to illustrate the sampling distribution: Suppose i have a spinner that is split evenly into 2 colors (blue and pink) and I want to know out of an innite number of spins what percentage of the times I will land on Blue. I take a sample of size 20 (I do this by spinning the spinner 20 times) and calculate the percentage of times I land on Blue out of the 20 spins. Population: An infinite number of spins I Parameter: proportion of all spins that land on Blue Sample: 20 spins Statistic: The proportion of the time I land on Blue out of a sample of 20 spins Notice this is a special case, I know the value of the parameter. Since the spinner is fair i know the parameter, p=.5. ' Claimzjhe theory says if we take multiple samples and plot the statistic from each sample, we should see a bell- shaped curve and peak at the parameter (0.50 or 50%). Notice this is a case where we know what the outcome should be if the theory is true. Often in statistics we can run simulations to see ifthe things we know are true match up with the theory as a check. So that when we don't know what the resuits should be, we feel comfortable relying on the theory. Mime 1. Please go to httgwwwshodommlinteractivatelactiwtiestBaslcSpinnerg Change the number of sections to 2, by pressing the -1 button twice. You should now see the spinner described above. Set the number of spins to 20 Click new experiment Click Spin Record the percentage of times the spinner landed on Blue, this is shown in the probability box under experimental. Repeat steps 4-6, 30 times record the resuits on the back of this page. i\" 57'5\"?!\" :4