Chapter 4.1, Problem 27E

To determine

To describe how non-response might lead to bias in this study and explain the likely direction of the bias.

Explanation of Solution

A total of $300$ people participated in a free twelve week weight loss course at a community health clinic. Then after one year administrators mailed all the people to see how much weight they had lost since the end of the course. But only $56$ participants responded.

Thus, according to this only a small proportion of the participants participated in the survey.

i.e., $\begin{array}{l}\frac{56}{300}=0.1867\\ =18.67\%\end{array}$

Thus, only $18.67\%$ of the people of the total participants participated in the survey. Thus the survey only considers a small amount of group which is less than $0.5$ in the survey. Thus the data considered is biased in nature and therefore it does not give true result of the actual weight loss by the people in the course and also the mean weight loss is also not true.