Simulate a sampling distribution. In Exercise 1.72

(page 41) and Example 4.26 (pages 213–214), you examined the density curve for a uniform distribution ranging from 0 to 1. The population mean for this uniform distribution is 0.5 and the population variance is 1•12. Let’s simulate taking samples of size 2 from this distribution.

Use the RAND() function in Excel or similar software to generate 100 samples from this distribution.

Put these in the first column. Generate another 100 samples from this distribution, and put these in the second column. Calculate the mean of the entries in the first and second columns, and put these in the third column.

Now, you have 100 samples of the mean of two uniform variables (in the third column of your spreadsheet).

(a) Examine the distribution of the means of samples of size two from the uniform distribution using your simulation of 100 samples. Using the graphical and numerical summaries that you learned in Chapter 1, describe the shape, center, and spread of this distribution.

(b) The theoretical mean for this sampling distribution is the mean of the population that we sample from. How close is your simulation estimate to this parameter value?

(c) The theoretical standard deviation for this sampling distribution is the square root of 1•24. How close is your simulation estimate to this parameter value?