Let Y, represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya,,Yin, of size n,, from the ith population with sample mean Y, and sample variance S7=(-)². (a) What is the distribution of Y,? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho: 4 = 140 Versus Ha Hiio when of is unknown and n, is small. (e) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a. (d) Define V₁, a function of St, that has a chi-square distribution.
Let Y, represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya,,Yin, of size n,, from the ith population with sample mean Y, and sample variance S7=(-)². (a) What is the distribution of Y,? State all the relevant parameters of the distribution. (b) Find a level a test (that is, the rejection region) for testing Ho: 4 = 140 Versus Ha Hiio when of is unknown and n, is small. (e) In the context of the test in part (b), state the Type I error and give a probability statement for the level of significance, a. (d) Define V₁, a function of St, that has a chi-square distribution.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Let Y, represent the ith normal population with unknown mean , and unknown variance
of for i=1,2. Consider independent random samples, Y₁₁, Y2Yin, of size n,, from
the ith population with sample mean Y, and sample variance S?=-(Yu-Y)²
(a) What is the distribution of Y,? State all the relevant parameters of the distribution.
(b) Find a level a test (that is, the rejection region) for testing Ho: 4 = 40 versus
Ha Pio when of is unknown and n, is small.
(e) In the context of the test in part (b), state the Type I error and give a probability
statement for the level of significance, a.
(d) Define V₁, a function of S7, that has a chi-square distribution.
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