# Question: A single observation of a random variable having a geometric

A single observation of a random variable having a geometric distribution is to be used to test the null hypothesis that its parameter equals θ0 against the alter-native that it equals θ1 > θ0. Use the Neyman-Pearson lemma to find the best critical region of size α.

## Answer to relevant Questions

Given a random sample of size n from a normal population with µ = 0, use the Neyman-Pearson lemma to construct the most powerful critical region of size α to test the null hypothesis σ = σ0 against the alternative σ = ...Decide in each case whether the hypothesis is simple or composite: (a) The hypothesis that a random variable has a Poisson distribution with λ = 1.25; (b) The hypothesis that a random variable has a Poisson distribution ...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. An education specialist is considering the use of instructional material on compact discs for a special class of third-grade students with reading disabilities. Students in this class are given a standardized test in May of ...The times to failure of certain electronic components in accelerate environment tests are 15, 28, 3, 12, 42, 19, 20, 2, 25, 30, 62, 12, 18, 16, 44, 65, 33, 51, 4, and 28 minutes. Looking upon these data as a random sample ...Post your question