TABLE 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
I = 106.4 hours II= 96.54 hours
SI = 10.3 hours SII = 13.4 hours
-Referring to Table 10-14, state the null and alternative hypotheses for testing if the population variances differ for preservatives I and II.

Question

TABLE 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
  I = 106.4 hours  II= 96.54 hours
SI = 10.3 hours SII = 13.4 hours
-Referring to Table 10-14, state the null and alternative hypotheses for testing if the population variances differ for preservatives I and II.
A) H₀: σI² ⁻ σII² ≥ 0 versus H₁: σI² - σII² < 0 
B) H₀: σI² ⁻ σII² ≤ 0 versus H₁: σI² - σII² > 0 
C) H₀: σI² ⁻ σII² = 0 versus H₁: σI² - σII² ≠ 0 
D) H₀: σI² ⁻ σII² ≠ 0 versus H₁: σI² - σII² = 0

Quizplus · Accepted Answer

The null hypothesis should state that the population variances are equal (i.e. σI² - σII² = 0) and the alternative should state that they are not equal (i.e. σI² - σII² ≠ 0). Choice C is the only option that reflects this. Choices A and B incorrectly assume that one population variance is larger than the other, and choice D reverses the null and alternative hypotheses.

TABLE 10-14 the Use of Preservatives by Food Processors Has Become a Become