Reference no: EM132351214

The goal of this mini-project is to help you verify the Rule for Sample Proportion firsthand, using a physical simulation. You will use the population represented in Figure 19.1 to do so. It contains 400 individuals, of whom 160 (40%) are X - that is, carry the gene for a disease -- and remaining 240 (60%) are O -- that is, do not carry the gene. You are going to draw 20 samples of size 15 from this population. Here are the steps you should follow:

Step 1: Develop a method for drawing simple random samples from this population. One way to do this is to cut up the symbols and put them all into a paper bag, shake well, and draw from the bag. There are less tedious methods, but make sure you actually get random samples. Explain your method.

Step 2: Draw a random sample of size of 15 and record the number and percentage who carry the gene. (sample proportion =  number who carry the gene/15)

Step 3: Repeat step 2 a total of 20 times, thus accumulating 20 samples, each of size 15. Make sure to start over each time; for example, if you used the methods of drawing symbols from a paper bag, then put the symbols back into the bag after each sample size 15 is drawn so they are available for the next sample as well.

Step 4: Create a stemplot or histogram of your sample proportions. Compute the mean. (for stemplot, the stem will be from 0.0, 0.1, 0.2 ...,0.9, the leaves will be 0, 1, 2 ...9 - which means 0.00 if 0/15 ...) You can google for how to draw stem-plot if you don't remember how to do it)

Step 5: Explain what the Rule for Sample Proportions tells you to expect for this situation. 

Step 6: Compare your results with what the Rule for Sample proportion tells you to expect. Be sure to mention mean, standard deviation, shape, and the intervals into which you expect 68%, 95%, 99.7% - almost all of the sample proportions to all.