The Return of the Random Rectangles
What you’ll need:a copy of Display 4.5, a method of producing random digits
1. Generate five distinct random numbers between 00 and 99.
2. Find the rectangles in Display 4.5 on page 233 that correspond to your random numbers. (The rectangle numbered 100 can be called 00.) This is your random sample of five rectangles.
3. Determine the areas of the rectangles in your random sample and find the sample median. (Save these five areas for step 7.)
Area of rectangles ______
Your Sample median ______
4. Combine your sample median with those of other students in the class and repeat steps 1 through 3 until you have 200 sample medians (many). Construct a plot showing the distribution of the 200 sample medians.
5. Describe the shape, mean, and standard error of this plot of sample medians. How do these compare to the shape, mean, and standard deviation of the population of areas in Display 7.2?
6. How does this sampling distribution compare to the simulated sampling distribution of the sample mean in Display 7.3?
7. Repeat steps 4 and 5, but this time use the maximum area of the five rectangles in each sample as the summary statistic. For example, if the areas in your sample are 1, 8, 4, 8, and 3, the maximum area is 8. (You can use the same samples as before.) You will also need to keep your data for E13.
Sample max area ______
8. Compare the population in Display 7.2 to the sampling distributions you plotted.
a. What is the median of the population of 100 rectangle areas? Is the sample median a good estimate of the median of the areas of all 100 rectangles?
b. What is the maximum of the population of 100 rectangle areas? Is the sample maximum a good estimate of the largest area of the 100 rectangles?
9. Reasonably likely and rare events. Use the plots you constructed to answer these questions.
a. What values of the sample median are reasonably likely? What values would be rare events?
b. What values of the sample maximum are reasonably likely? What values would be rare events?
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