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Statistics: finding a critical region

  1. Apr 4, 2013 #1
    Let X1, X2, …, X10 be a random sample of size ten from the Normal(3, σ^2) distribution.
    (a) Use the likelihood ratio test to derive a 5%-level critical region for testing H0 : σ^2 = 1
    versus H1 : σ^2 ≠ 1.
    (b)Suppose the following ten values from the Normal(3, σ^2) distribution are observed. Do we
    reject the null hypothesis H0 : σ^2 = 1 at 5%-level? Please justify your answer.
    2.82, 2.35, 3.74, 1.93, 4.51, 3.17, 1.41, 4.23, 4.77, 3.89
  2. jcsd
  3. Apr 5, 2013 #2


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    Science Advisor

    Hey Aria1.

    What is the definition of the LRT? (Hint: It involves the MLE likelihood and the likelihood of the null hypothesis).
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