The Irradiation of Food to Destroy Bacteria Is an Increasingly

question 19

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. $$\begin{array} { | c | c | } \hline \text { Method 1 } & \text { Method 2 } \\\hline \bar { x } _ { 1 } = 86 & \bar { x } _ { 2 } = 98 \\\hline s _ { 1 } ^ { 2 } = 324 & s _ { 2 } ^ { 2 } = 841 \\\hline\end{array}$$ a. Estimate with 95% confidence the ratio of the variances of the bacteria counts under the two methods, and briefly describe what the interval estimate tells you.
b. Do these results allow us to infer at the 5% significance level that there is a difference in bacteria count between methods 1 and 2?
c. Do these results allow us to infer at the 5% significance level that the mean bacteria count with method 1 is less than 95?

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Definitions:

Benevolent Assimilation

A policy described by President McKinley regarding the Philippines, aiming to assimilate Filipinos into American culture and governance with a supposedly benevolent approach.

Emilio Aguinaldo

A Filipino revolutionary, politician, and military leader who played a significant role in the Philippine struggle for independence from Spain and later against United States colonization.

United Fruit Company

An American corporation that was a major player in the fruit industry, primarily bananas, and had significant influence in Central American countries.

Honduras

A country in Central America with a diverse culture and geography, known for its rich natural resources, including forests, minerals, and agricultural produce.