# Question

Use the Sampling Distributions applet. Set the population to Binary, p = 0.6. The graph of the population distribution for a categorical variable with p , the population proportion, equal to 0.60 should appear. Let’s simulate a sample of size n = 100 from this population. Set n = 100, then click on Sample.
a. Using the second graph and the numerical summary to the side of the graph, how does the data distribution (the sample data) compare to the population distribution represented in the first graph?
b. Let’s simulate 1000 samples of size n = 100 from this population. Set N = 1000. Then click on Sample. Let’s first consider the counts of the successes (sum of the 1s) from each sample. Go to the third graph. This is a histogram of all the counts or number of successes in each simulated sample (there should be a total of 1001 samples) along with descriptive statistics in the box to the left of the third graph.
Describe the shape, center (mean), and variability (standard deviation) of this distribution. This is a sampling distribution of counts with n = 100. What would you expect for the shape, mean and standard deviation of this sampling distribution of counts? How do these expected values compare to your simulated values?
c. Let’s work with the proportions instead of counts. Go to the fourth graph. This is a histogram of all the sample proportions of 1s (successes) in each simulated sample along with descriptive statistics.
Describe the shape, center (mean), and variability (standard deviation) of the distribution. Note that this is a sampling distribution of sample proportions with n = 100. What would you expect for the shape, mean and standard deviation of this sampling distribution of the sample proportion? How do these expected values compare to your simulated values?
d. Compare the simulated sampling distribution of sample proportions to the simulated sampling distribution of counts with respect to shape, the means, and the standard deviations.

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