5.63 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).
5.63
Software, answers will vary. (a) The shape should be roughly Normal. (b) The mean should be close to 0.5. (c) The standard deviation should be close to .