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, suppose α = 0.05. Which of the following represents the result of the relevant hypothesis test?
A) The alternative hypothesis is rejected.
B) The null hypothesis is rejected.
C) The null hypothesis is not rejected.
D) Insufficient information exists on which to make a decision.

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, suppose α = 0.05. Which of the following represents the result of the relevant hypothesis test?
A) The alternative hypothesis is rejected. 
B) The null hypothesis is rejected. 
C) The null hypothesis is not rejected. 
D) Insufficient information exists on which to make a decision.

Quizplus · Accepted Answer

We need to perform a two-sample t-test for the means of the two populations, assuming equal variances, with a significance level of 0.05. The t-test statistic is calculated to be -1.96, which falls within the acceptance region of -2.048 < t < 2.048 (calculated using the degrees of freedom = 28 and a two-tailed test). Therefore, we fail to reject the null hypothesis that there is no difference between the means of the two populations, and conclude that there is not enough evidence to support the claim that one preservative is more effective than the other in retarding spoilage.

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