What You Ll Need: Display 4.5, a Method of Producing Random Digits

Random Rectangles

What you’ll need: Display 4.5, a method of producing random digits

Your goal is to choose a sample of 5 rectangles from which to estimate the average area of the 100 rectangles in Display 4.5.

1. Without studying the display of rectangles too carefully, quickly choose five that you think represent the population of rectangles on the page. This is your judgment sample.

2. Find the areas of each rectangle in your sample of five and compute the sample mean, that is, the average area of the rectangles in your sample.

3. List your sample mean with those of the other students in the class. Construct a plot of the means for your class.

4. Describe the shape, center, and spread of the plot of sample means from the judgment samples.

Unit number ______

Area of each rectangle ______

Mean Area ______

5. Now generate five distinct random integers between 0 and 99. (The rectangle numbered 100 can be called 0.) Find the rectangles whose numbers correspond to your random numbers. This is your random sample of five rectangles. [You can use a calculator to generate random numbers. See Calculator Note 4A.] Or see the random number table attached.

6. Repeat steps 2–4, this time using your random sample.

Unit number ______

Area of each rectangle ______

Mean Area ______

7. Discuss how the two distributions of sample means are similar and how they different.

8. Which method of producing sample means do you think is better if the goal is to use the sample mean to estimate the population mean? (I have the value of the population mean.)

D9. Use a table of random digits to take a simple random sample of six students from your class. For what characteristics is the sample representative of this class? Not representative?

D10. Describe how you could obtain a simple random sample of all students enrolled in the English classes at your school.

D11. Readability. You’ve decided you simply must know the proportion of capital letters in this textbook because it can indicate the complexity of the sentences on a page. Think of the book itself as your population and each printed character as a unit. How could you get a simple random sample of 10,000 characters? What are the advantages and disadvantages of this sampling method?