# Question

The purpose of this mini-project is to help you verify the Rule for Sample Means, using a physical simulation. Suppose you are interested in measuring the average amount of blood contained in the bodies of adult women, in ounces. Suppose, in truth, the population consists of the following listed values. (Each value would be repeated millions of times, but in the same proportions as they exist in this list.) The actual mean and standard deviation for these numbers are 110 ounces and 5 ounces, respectively. The values are bell-shaped.

Population Values for Ounces of Blood in Adult Women

Step 1: Develop a method for drawing simple random samples from this population. One way to do this is to write each number on a slip of paper, put all the slips into a paper bag, shake well, and draw from the bag. If a number occurs multiple times, make sure you include it that many times. Make sure you actually get random samples. Explain your method.

Step 2: Draw a random sample of size 9. Calculate and record the mean for your sample.

Step 3: Repeat step 2 a total of 20 times, thus accumulating 20 samples, each of size 9. Make sure to start over each time; for example, if you drew numbers from a paper bag, put the numbers back after each sample of size 9 so they are available for the next sample as well.

Step 4: Create a stemplot or histogram of your 20 sample means. Compute the mean of those sample means.

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

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

Population Values for Ounces of Blood in Adult Women

Step 1: Develop a method for drawing simple random samples from this population. One way to do this is to write each number on a slip of paper, put all the slips into a paper bag, shake well, and draw from the bag. If a number occurs multiple times, make sure you include it that many times. Make sure you actually get random samples. Explain your method.

Step 2: Draw a random sample of size 9. Calculate and record the mean for your sample.

Step 3: Repeat step 2 a total of 20 times, thus accumulating 20 samples, each of size 9. Make sure to start over each time; for example, if you drew numbers from a paper bag, put the numbers back after each sample of size 9 so they are available for the next sample as well.

Step 4: Create a stemplot or histogram of your 20 sample means. Compute the mean of those sample means.

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

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

## Answer to relevant Questions

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