21.4 Exercises

Selected answers are available in Sect. D.20.

Exercise 21.1 A researcher was computing a 95% CI for a single proportion to estimate the proportion of trees with apple scabe (Hirst and Stedman 1962), and found that $\hat{p}=0.314$ and $\text{s.e.}\left(\hat{p}\right)=0.091$.

What is wrong with the following conclusion that the researcher made?

The approximate 95% CI for the sample proportion is between 0.223 and 0.405.

Exercise 21.2 A researcher was computing a 95% CI for a single proportion to estimate the proportion of trees with apple scabe (Hirst and Stedman 1962), and found that $\hat{p}=0.314$ and $\text{s.e.}\left(\hat{p}\right)=0.091$.

What is wrong with the following conclusion that the researcher made?

This CI means we are 95% confident that between 22.3 and 40.5 trees are infected with apple scab.