Instruction 10-9
The use of preservatives by food processors has become a controversial issue. Suppose two preservatives are
extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative A and 15 are treated with preservative B, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarised in the table below.
$$\begin{array} { c c }
\text { Preservative A } & \text { Preservative B } \
\bar { X } _ { A } = 106.4 \mathrm { hours } & \bar { X } _ { \mathbf { B } } = 56.54 \mathrm { hours } \
S _ { A } = 10.3 \mathrm { hours } & S _ { \mathrm { B } } = 13.4 \mathrm { hours }
\end{array}$$
-Referring to Instruction 10-9,state the test statistic for determining if the population variances differ for preservatives A and B
A) = -3.10
B) = 0.8250
C) = 0.5908
D) = 0.7687

Question

Instruction 10-9
The use of preservatives by food processors has become a controversial issue. Suppose two preservatives are
extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative A and 15 are treated with preservative B, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarised in the table below.
 $$\begin{array} { c c } 
\text { Preservative A } & \text { Preservative B } \
\bar { X } _ { A } = 106.4 \mathrm { hours } & \bar { X } _ { \mathbf { B } } = 56.54 \mathrm { hours } \
S _ { A } = 10.3 \mathrm { hours } & S _ { \mathrm { B } } = 13.4 \mathrm { hours }
\end{array}$$
-Referring to Instruction 10-9,state the test statistic for determining if the population variances differ for preservatives A and B
A) = -3.10
B) = 0.8250
C) = 0.5908
D) = 0.7687

Quizplus · Accepted Answer

The test statistic for comparing variances (population variances) is the ratio of the two sample variances. Given $S_A^2 = 10.3^2$ and $S_B^2 = 13.4^2$, the test statistic is $\frac{S_A^2}{S_B^2} = \frac{10.3^2}{13.4^2} = \frac{106.09}{179.56} = 0.5908$.

Instruction 10-9 the Use of Preservatives by Food Processors Has

Instruction 10-9
the Use of Preservatives by Food Processors Has