STAT 202 Compare the normal and binomial distributions
We will compare the normal and binomial distributions for various n.
a) Simulate a binomial data set by doing the following: “Data”→ “Simulate” →“Binomial”.
Use the following settings: “n” (insert 50), “p” (insert .08), “columns” (insert 1), and “rows” (insert 150).
b) Compute and .
c) Compute the expected mean,, and standard deviation ,.
d) Create a histogram of your simulated binomial data.
Use the option “Overlay density”, choose Normal, and use the settings for “mean” and “Std. Dev” which you computed in step c.
Repeat the steps above, replacing “n” with 100, then with 1000. Be sure to use the same bin width on all of your histograms. You do not need to answer Question 7 again for each trial.
Question #7: Compare the 3 histograms. What do you observe as the number of data points, n, increases? Does this correspond with your calculations for step b?Response:
Use StatCrunch to compute the mean and standard deviation of the data in each of the three columns. These are the sample mean values.
Question #8: Examine the mean values. Compare the expected mean values with the sample mean values. Discuss the results. Are some estimates better than others? Is this surprising?
Question #9: Repeat the previous question for standard deviation.