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. $$\begin{array} { | c | c | }
\hline \text { Method 1 } & \text { Method 2 } \
\hline \bar { x } _ { 1 } = 86 & \bar { x } _ { 2 } = 98 \
\hline s _ { 1 } ^ { 2 } = 324 & s _ { 2 } ^ { 2 } = 841 \
\hline
\end{array}$$ Estimate with 95% confidence the difference in the mean bacteria counts between method 1 and method 2.

Question

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. $$\begin{array} { | c | c | } 
\hline \text { Method 1 } & \text { Method 2 } \
\hline \bar { x } _ { 1 } = 86 & \bar { x } _ { 2 } = 98 \
\hline s _ { 1 } ^ { 2 } = 324 & s _ { 2 } ^ { 2 } = 841 \
\hline
\end{array}$$ Estimate with 95% confidence the difference in the mean bacteria counts between method 1 and method 2.

Quizplus · Accepted Answer

The Answer of 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. $$\begin{array} { | c | c | } 
\hline \text { Method 1 } & \text { Method 2 } \
\hline \bar { x } _ { 1 } = 86 & \bar { x } _ { 2 } = 98 \
\hline s _ { 1 } ^ { 2 } = 324 & s _ { 2 } ^ { 2 } = 841 \
\hline
\end{array}$$ Estimate with 95% confidence the difference in the mean bacteria counts between method 1 and method 2.

The Irradiation of Food to Destroy Bacteria Is an Increasingly