Question: Modify Theorem 11 1 so that it can be used to
Modify Theorem 11.1 so that it can be used to appraise the maximum error when σ2 is unknown. This method can be used only after the data have been obtained.
Answer to relevant QuestionsState a theorem analogous to Theorem 11.1, which enables us to appraise the maximum error in using 1 – 2 as an estimate of µ1 – µ2 under the conditions of Theorem 11.4. Use the Neyman-Pearson lemma to indicate how to construct the most powerful critical region of size α to test the null hypothesis θ = θ0, where θ is the parameter of a binomial distribution with a given value of n, ...In the solution of Example 12.6, verify the step that led to Show that for k = 2 the likelihood ratio statistic of Exercise 12.25 can be expressed in terms of the ratio of the two sample variances and that the likelihood ratio test can, therefore, be based on the F distribution. Suppose that we want to test the null hypothesis that an antipollution device for cars is effective. (a) Explain under what conditions we would commit a type I error and under what conditions we would commit a type II ...
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