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What values of the generalized likelihood ratio A are necessary to reject the null hypothesis at the significance level  = .1 if the degrees of freedom are 1, 5, 10, and 20?

This problem introduces a Bayesian perspective on the likelihood ratio, which will be expanded upon in chapter 15. According to the Bayesian model, one's belief in a hypothesis is represented as a probability; in this manner let P(H₁) and P(H₂) represent an experimenter's belief in two incompatible hypotheses prior to gathering data, X. They are called prior probabilities. Having observed X, the probabilities change to P(H₁IX) and P(H₂IX), which are called posterior probabilities. Show that

that is, that to find the ratio of posterior probabilities; the ratio of prior probabilities is multiplied by the likelihood ratio. In the case that H₂ is the hypothesis that H1is false, the ratios are the prior and posterior odds of H₁.