Problem The Medco pharmaceutical company has just developed a new antibiotic. Two percent of children taking competing antibiotics experience headaches as a side effect. A researcher for the Food and Drug Administration wishes to know if the percentage of children taking the new antibiotic who experience a headache as a side effect is more than \(2 \%\). The researcher conducts a hypothesis test with \(H_{0}: p=0.02\) and \(H_{1}: p>0.02\). Explain what it would mean to make a

(a) Type I error and

(b) Type II error.

Approach A Type I error occurs if we reject the null hypothesis when it is true. A Type II error occurs if we do not reject the null hypothesis when the alternative hypothesis is true.