# 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.

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.

## Answer to relevant Questions

Consider the sampling distribution you were simulating in parts a and b of the previous exercise, assuming p = 0.10 with samples of size 4000 each. Using the appropriate formulas from this section, find the mean and the ...Suppose a baseball player has a 0.200 probability of getting a hit in each time at-bat. a. Describe the shape, mean, and standard deviation of the sampling distribution of the proportion of times the player gets a hit after ...According to recent General Social Surveys, in the United States the population distribution for adults of X = number of sex partners in the past 12 months has a mean of about 1.0 and a standard deviation of about 1.0. a. ...As the sample size increases, the standard deviation of the sampling distribution of x increases. Explain your answer. A study dealing with health care issues plans to take a sample survey of 1500 Americans to estimate the proportion who have health insurance and the mean dollar amount that Americans spent on health care this past year. a. ...Post your question

0