Question: A random sample of size n from an exponential population
A random sample of size n from an exponential population is used to test the null hypothesis θ = θ0 against the alternative hypothesis θ = θ1 > θ0. Use the Neyman-Pearson lemma to find the most powerful critical region of size α, and use the result of Example 7.16 on page 222 to indicate how to evaluate the constant.
Answer to relevant QuestionsUse 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, ...With reference to Exercise 12.3, suppose that we had wanted to test the null hypothesis k ≤ 2 against the alternative hypothesis k > 2. Find the probabilities of (a) Type I errors for k = 0, 1, and 2; (b) Type II errors ...For the likelihood ratio statistic of Exercise 12.22, show that –2 ∙ ln λ approaches t2 as n → ∞. In exercise A random sample of size n from a normal population with unknown mean and variance is to be used to test ...The average drying time of a manufacturer’s paint is 20 minutes. Investigating the effectiveness of a modification in the chemical composition of her paint, the manufacturer wants to test the null hypothesis µ = 20 ...The sum of the values obtained in a random sample of size n = 5 is to be used to test the null hypothesis that on the average there are more than two accidents per week at a certain intersection (that λ > 2 for this Poisson ...
Post your question