# Math 302

## Writing Assignment 2: Understanding the Bootstrap

### The parametric bootstrap

The lecture notes and handouts describe how to apply the bootstrap to estimate a parameter `p` from a geometric distribution.

In practicing for "April Madness", the Department of Mathematics and Computer Science basketball tournament, a professor finishes each practice by shooting three point baskets until making one. Assume that practice does not improve the professor's accuracy, and that the outcomes of all shots are independent. Over a three week period, the professor practices fifteen times and records the number of attempts until making a shot. Click here for the data.

Use the parametric bootstrap to construct a 95% confidence interval for the probability the professor makes a three point basket.

### The nonparametric bootstrap

The lecture notes and handouts describe how to use the nonparametric bootstrap to estimate the uncertainty in the estimate of a population mean.

All foods are required by law to report the number of calories per serving. Investigators believe that "diet" foods may be erroneously labeled. The investigators take a random sample of forty "diet" foods, use a bomb calorimeter to compute the appropriate number of calories per serving, and calculate the relative difference between the measured amount and the label amount. 100% x (measured - labeled)/labeled. A positive relative difference indicates that the product actually contains more calories than labeled. Click here for the data.

Use the nonparametric bootstrap to estimate the median relative difference between measured calories and labeled calories in "diet" foods.

Commented S-PLUS code to carry out these bootstrap computations is in this script file.

The data from the calorie example originated in the Data and Story Library of Statlib (`http://www.stat.cmu.edu`).