The Irradiation of Food to Destroy Bacteria Is an Increasingly

question 78

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?

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Definitions:

Hereditary Genius

A concept suggesting that genius or exceptional ability is inherited genetically from one's ancestors.

Francis Galton

A British polymath who made significant contributions to fields like statistics, psychology, and genetics, often considered a pioneer in the study of human intelligence.

Genetic Inheritance

The process by which genetic information is passed from parents to their offspring, determining traits.

Normal Distribution

A symmetrical, bell-shaped distribution of data in which most of the data points are concentrated around the mean, with the tails of the distribution tapering off symmetrically at both ends.