Samples of peanut butter produced by 2 different manufacturers are tested for aflatoxin content, with the following results:

(a) Use analysis of variance to test whether the two brands differ in aflatoxin content.

(b) Test the same hypothesis using a two sample \(t\) test.

(c) We have shown on page 212 that the \(t\) statistic with \(v\) degrees of freedom and the \(F\) statistic with 1 and \(v\) degrees of freedom are related by the formula \[F(1, v)=t^{2}(v)\]
Using this result, prove that the analysis of variance and two sample \(t\) test methods are equivalent in this case.

Transcribed Image Text:

Aflatoxin Content (ppb) Brand A Brand B 0.5 4.7 0.0 6.2 3.2 0.0 1.4 10.5 0.0 2.1 1.0 0.8 8.6 2.9