Question

25. Independent random samples o n from k normal w variances are to be used to test the hu σί against the alternati ations with unknown means and . . alternative that these variances are not all equal. (a) Show that under the nul hypothesis i the variances likelihood estimates of the means ,41 an and the va are (ni-1)si /n に1 σ2 anded eel. while σ,-are where n Σ ni, while with out restrictions the maximum likelihood estimates of the means nces and the v ara (h) Using the results of part (a), show that the likelihood ratio statistic can be written as n/2 (n,- 1)s i-1

Answer 1

hoomal pap iith unknawn means Le一Pdt-ot - Normal dista, bution is 2 Cansides likelihood 2, aist alt Naud 2

2. ST 2L 2. k'의 nt bs izelihoad aatia test statistic is 2.1h ru