# Math 225

## Introduction to Biostatistics

### Exercise 9-5

The purpose of the study is to see how smoking history affects physical fitness as measured by the response in minutes until an individual reaches maximum oxygen uptake for three different stress tests.

1. Calculate the mean of each of the nine groups and make an interaction plot. Does there appear to be a strong interaction between test and smoking history?

2. Consider the ANOVA table below. Are there differences in the stress tests effects on the response? Are there different effects on the response due to smoking status? Does tehre appear to be an interaction between stress test and smoking status on the response?

3. Find a single number that is our best estimate of the size of a typical deviation of an observation from its group mean.

Here is the ANOVA table for the data in exercise 9-5.
```           Df Sum of Sq  Mean Sq  F Value     Pr(F)
test  2  298.0719 149.0359 45.27928 0.0000001
smoke  2   84.8985  42.4493 12.89670 0.0003348
test:smoke  4    2.8148   0.7037  0.21380 0.9273412
Residuals 18   59.2467   3.2915
```