# Math 1223 13 Bootstrapping

The phrase “You dirty rat” does rats a disservice. In a recent study, rats showed compassion that surprised scientists. Twenty-three of the thirty rats in a study freed another trapped rat from in their cage, even when chocolate served as a distraction and even when rats would have to share their chocolate with their companion. We wish to use the sample to estimate the proportion of rats to show empathy in this way.

1. Give the relevant parameter and its point estimate.

2. Describe how to use 30 slips of paper to create one bootstrap statistic. BE SPECIFIC!

3. Use Excel to create a bootstrap distribution with 50 entries. Describe the shape and center of the bootstrap distribution.

4. What is the standard error?

5. Use the standard error to find and interpret a 95% confidence interval for the proportion of rats likely to show empathy.

6. Construct and interpret a 90% confidence interval.

7. Construct and interpret a 99% confidence interval.

Utilizing the excel file included with this assignment, you will find discover the bootstrap mean and confidence interval for the sale price of homes.

8. Give the relevant parameter and its point estimate.

9. Describe how to use slips of paper to create one bootstrap statistic. How did this differ from the previous strips of paper?

10. Use Excel to create a bootstrap distribution with 50 entries. Describe the shape and center of the bootstrap distribution.

11. What is the standard error?

12. Use the standard error to find and interpret a 95% confidence interval for the mean sale price of homes.

13. Construct and interpret a 90% confidence interval.

14. Construct and interpret a 99% confidence interval.

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