A food processor wants to compare two preservatives for their effects on retardi

Question

A food processor wants to compare two preservatives for their effects on retarding spoilage. Suppose 10 cuts of fresh meat are treated with preservative A and 10 cuts are treated with preservative B. and the time (in hours) until spoilage begins is recorded for each of the 20 cuts. The results are summarized in the following table. (a) State clearly the null and alternative hypotheses to determine if the average time until spoilage begins differs for preservatives A and B. (b) Compute the pooled variance and the value of the test statistic. (c) Determine the rejection region at alpha =.05, and write down a proper conclusion.

Explanation / Answer

answer a)

null hypothesis H0:there is no difference in average time until spoilage begins for preservatives A and B

alternative H1:there is difference in average time until spoilage begins for preservatives A and B

answer b) pooled variance sp2=((n1-1)s12+(n2-1)s22)/n and n=n1+n2-2

nere n1=n2=20

sp2=((20-1)*90.25+(20-1)*132.25)/38=111.25

sp=sqrt(111.25)=10.56

t=|(mean1-mean2)|/(sp/n1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and n=n1+n2-2

t=|(9.5-11.5)|/(10.56/sqrt(38)=1.17

answer c)

critical t(0.05,38)=2.02

rejection region t>2.02

calculated t-statistic 1.17 is less than the critical value, therefore we reject to fail null hypothesis and conclude that

:there is no difference in average time until spoilage begins for preservatives A and B

A B mean 108.7 98.7 s 9.5 11.5 s2 90.25 132.25 n 20 20

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