SCENARIO 10-14
the Use of Preservatives by Food Processors Has

question 220

Short Answer

SCENARIO 10-14
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 I and 15 are treated with preservative II, and the number of hours until
spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table
below.
Preservative I Preservative II $\begin{array}{ll}\text { Preservative I } & \text { Preservative II } \\\bar{X}_{\mathrm{I}}=106.4 \text { hours } & \bar{X}_{\mathrm{II}}=96.54 \text { hours } \\S_{\mathrm{I}}=10.3 \text { hours } & S_{\Pi}=13.4 \text { hours }\end{array}$

-Referring to Scenario 10-14, state the null and alternative hypotheses for testing if the population variances differ for preservatives I and II. a) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \geq 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } < 0$
b) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \leq 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } > 0$
c) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } = 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \neq 0$
d) $H _ { 0 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } \neq 0$ versus $H _ { 1 } : \sigma _ { I } ^ { 2 } - \sigma _ { I I } ^ { 2 } = 0$

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