B2. Consider the testing problem where we have observed a random sample x₁,...,n fromthe model X₁,..., Xn ~ N(µ, o²), where the X, are independent, and we want to testthe hypothesis Ho: o² = o against the alternative H₁: 0² o. For the test we usethe test statisticny = Σi=1(x₁ - x)²0²where is the sample mean of the ₁.(a) What are the type I errors and type II errors in this testing problem?(b) If Ho is true, what is the distribution of the random variable Y corresponding to y?(c) Assume that n = 20 and we reject Ho if and only if y> 32.852. What is theprobability of a type I error in this case?(d)now that H₁ is true for the test in part (c). Draw a sketch of the type IIerror as a function of o2. (There is no need to calculate explicit values.)-(e) Explain why the test described in part (c) is not a good test for testing the hypoth-esis Ho: 0² o against the alternative H₁: o² o2. How would you improvethe test?

As per our guidelines, we are supposed to answer only 3 sub-parts.In this problem we are performing…

Answered: B2. Consider the testing problem where…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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ISBN:9780079039897

Author:Carter

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Chapter10: Statistics

Section10.1: Measures Of Center

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Let Y, represent the ith normal population with unknown mean 44, and unknown variance of for i 1,2. Consider independent random samples, Ya, Y₁2,,Yin, of size ni, from the ith population with sample mean Y, and sample variance S?=1Σj=1(Y₁j - Y₁². (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 : μi = μio versus Ha: Pipio when of is unknown and n, is small. (c) 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.
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Q2.[5 points]: Two random samples taken from two normal populations yielded the following information: Sample Sample size Sample variance si = 53 s를 %3D32 1 n1 = 16 n2 = 21 i. Find the test statistic F Find the degrees of freedom dfl and df2. Perform the test the hypotheses H,:o = ož vs. H,:o > ož at the 5% level of significance. ii. iii.
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