The Irradiation of Food to Destroy Bacteria Is an Increasingly

question 90

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:

Management Costs

Expenses associated with directing and controlling a business or organization.

Organic Design

A management and organizational structure approach emphasizing adaptability, teamwork, and decentralized decision-making.

Decentralized Authority

An organizational structure in which decision-making authority is distributed among various levels and departments, rather than being concentrated at a central point.

Narrow Spans of Control

An organizational structure where each manager has a limited number of direct reports, allowing for more intimate supervision and engagement.