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?

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. $$\begin{array} { | c | c | } 
\hline \text { Method 1 } & \text { Method 2 } \
\hline \bar { x } _ { 1 } = 86 & \bar { x } _ { 2 } = 98 \
\hline s _ { 1 } ^ { 2 } = 324 & s _ { 2 } ^ { 2 } = 841 \
\hline
\end{array}$$ 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?

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. $$\begin{array} { | c | c | } 
\hline \text { Method 1 } & \text { Method 2 } \
\hline \bar { x } _ { 1 } = 86 & \bar { x } _ { 2 } = 98 \
\hline s _ { 1 } ^ { 2 } = 324 & s _ { 2 } ^ { 2 } = 841 \
\hline
\end{array}$$ 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?

The Irradiation of Food to Destroy Bacteria Is an Increasingly