Question

PLEASE PROVIDE A SPREADSHEET FOR EACH PART FOR PERSONAL REFERENCE

Part 1:

Using Excel’s Randbetween(0,9) function, generate 200 samples of five random numbers between 0 and 9, calculate the mean of each sample. Show me the list of the 200 means. Typically, they should look like: 4.8, 3.6, 4.4, 6.0, etc.

Part 2:

Using Excel, calculate the overall mean of the 200 sample means (the average of the averages). This should be around 4.5.

Part 3:  

Using Excel, calculate the standard error of the mean (SEM) (i.e. the standard deviation of the 200 sample means). We established in the previous simulation that the population average is 4.5 and the standard deviation of the population is 2.87.

Since the SEM= ^σ= σ/√n. The SEM therefore is 1.28. Thus, the standard deviation of the 200 sample means should be approximately 1.28.

Part 4:

Using Excel, make the histogram of the 200 sample means (sampling distribution of the mean) (use interval size 1, i.e., 0-1, 1-2, 2-3, …8-9). According to the Central Limit Theorem a bell shaped curve should appear. Show me this graph.

Part 5:

Discuss the intuitive logic of the Central Limit Theorem. Discuss the implications of part 4 in this context. (My videos might help here.)

Answer 1

First 20 samples of the total 200 samples generated:

Mean=4.457, SD=1.282