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Lecture

# Tutorial9.pdf

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School
Department
Statistics
Course
STAT 330
Professor
Christine Dupont
Semester
Fall

Description
Stat 330 - Tutorial 9 1. Suppose X ;1::;X n ▯ N(▯;▯ ) where ▯ is known. Suppose we would like to test H : 0 ▯ = ▯ 0s H :A▯ 6= ▯ .0 (a) Construct the LR test statistic under H0. (b) Show that the ▯ distribution is the exact distribution of the test statistic under0H . 1 (c) Conduct the test when ▯ =05 at a 5% signiﬁcance level. You are given that n = 10, P n 2 i=1 xi= 58 and ▯ = 2. Note also that P(▯ >13:8415) = 0:05. (d) Disregard part c). Find the values of ▯0such that H 0ill not be rejected at a signiﬁ- cance level of ▯. 2. The following model is proposed for the distribution of family size in a large population: k ▯ P(k children in family; ▯) = ▯ , for k
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