A sampling applet experiment. The Simple Random Sample applet can animate the idea of a sampling distribution. Form a population labeled 1 to 100.We will choose an SRS of 10 of these numbers. That is, in this exercise the numbers themselves are the population, not just labels for 100 individuals. The proportion of the whole numbers 1 to 100 that are equal to or less than 60 is p = 0.6. This is the population proportion.

(a) Use the applet to choose an SRS of size 25. Which 25 numbers were chosen? Count the numbers ≤ 60 in your sample and divide this count by 25. This is the sample proportion ˆp.

(b) Although the population and the parameter p = 0.6 remain fixed, the sample proportion changes as we take more samples.

Take another SRS of size 25. (Use the “Reset” button to return to the original population before taking the second sample.) What are the 25 numbers in your sample? What proportion of these is

≤ 60? This is another value of ˆp.

(c) Take 8 more SRSs from this same population and record their sample proportions. You now have 10 values of the statistic

ˆp from 10 SRSs of the same size from the same population. Make a histogram of the 10 values and mark the population parameter p = 0.6 on the horizontal axis. Are your 10 sample values roughly centered at the population value p? (If you kept going forever, your ˆp-values would form the sampling distribution of the sample proportion; the population proportion p would indeed be the center of this distribution.)