Question 5.62

5.62 Simulate a sampling distribution for .

In the previous exercise, you were asked to use statistical software’s capability to generate Poisson counts. Here, you will use software to generate binomial counts from the distribution. We can use this fact to simulate the sampling distribution for . In this exercise, you will generate 1000 sample proportions for and .

  • JMP users: With a new data table, right-click on header of Column 1 and choose Column Info. In the drag-down dialog box named Column Properties, pick the Formula option. You will then encounter a Formula dialog box. Find and click in the Random Binomial function into the dialog box. Proceed to give the values of 100 for and 0.7 for . Thereafter, click the division symbol found the calculator pad, and divide the binomial function by 100. Click OK twice to return to the data table. Finally, right-click on any cell of the column holding the formula, and choose the option of Add Rows. Input a value of 1000 for the number of rows to create and click OK. You will find 1000 sample proportions generated.
  • Minitab users: Calc → Random Data → Binomial. Enter 1000 in the Number of row of data to generate dialog box, type “c1” in the Store in column(s) dialog box, enter 100 in the Number of trials dialog box, and enter 0.7 in the Event probability dialog box. Click OK to find the random binomial counts in column c1. Now use Calculator to define another column as the binomial counts divided by 100.
  1. Produce a histogram of the randomly generated sample proportions, and describe its shape.
  2. What is the sample mean of the 1000 proportions? How close is this simulation estimate to the parameter value?
  3. What is the sample standard deviation of the 1000 proportions? How close is this simulation estimate to the theoretical standard deviation?