5.15 Use the Simple Random Sample applet. The Simple Random Sample applet can illustrate the idea of a sampling distribution. Form a population labeled 1 to 100. We will choose an SRS of 15 of these numbers. That is, in this exercise, the numbers themselves are the population, not just labels for 100 individuals. The mean of the whole numbers 1 to 100 is 50.5. This is the parameter, the mean of the population.

1. (a) Use the applet to choose an SRS of size 15. Which 15 numbers were chosen? What is their mean? This is a statistic, the sample mean .

2. (b) Although the population and its mean 50.5 remain fixed, the sample mean changes as we take more samples. Take another SRS of size 15. (Use the “Reset” button to return to the original population before taking the second sample.) What are the 15 numbers in your sample? What is their mean? This is another value of .

3. (c) Take 18 more SRSs from this same population and record their means. You now have 20 values of the sample mean from 20 SRSs of the same size from the same population. Make a histogram of the 20 values and mark the population mean 50.5 on the horizontal axis. Are your 20 sample values roughly centered at the population value? (If you kept going forever, your -values would form the sampling distribution of the sample mean; the population mean would indeed be the center of this distribution.)