The Irradiation of Food to Destroy Bacteria Is an Increasingly

Essay

The irradiation of food to destroy bacteria is an increasingly common practice. In order to determine which one of two methods of irradiation is best, a scientist took a random sample of 100 one-kilogram packages of minced meat and subjected 50 of them to irradiation method 1 and the remaining 50 to irradiation method 2. The bacteria counts were measured and the following statistics were computed. The scientist noted that the data were normally distributed. $$\begin{array} { | c | c | } \hline \text { Method 1 } & \text { Method 2 } \\\hline \bar { x } _ { 1 } = 86 & \bar { x } _ { 2 } = 98 \\\hline s _ { 1 } ^ { 2 } = 324 & s _ { 2 } ^ { 2 } = 841 \\\hline\end{array}$$ An important factor in determining which method to choose is consistency. That is, all other things being equal, we would prefer to have a method that leaves all irradiated food with approximately the same bacteria count. Can we infer at the 5% significance level that method 1 is superior to method 2 in this respect?