Question:
Let X1, X2 , … , X9 be a random sample from a N(μ, σ2) distribution, where μ ∈ \(\R\) and σ > 0 are unknown. Let the observed values of \(\overline{X}=\frac{1}{9}\sum^9_{i=1}X_i\) and \(S^2=\frac{1}{8}\sum^9_{i=1}(X_i-\overline{X})^2\) be 9.8 and 1.44, respectively. If the likelihood ratio test is used to test the hypothesis H0 : μ = 8.8 against H1 : μ > 8.8, then the p-value of the test equals __________ (round off to 3 decimal places)
Let X1, X2 , … , X9 be a random sample from a N(μ, σ2) distribution, where μ ∈ \(\R\) and σ > 0 are unknown. Let the observed values of \(\overline{X}=\frac{1}{9}\sum^9_{i=1}X_i\) and \(S^2=\frac{1}{8}\sum^9_{i=1}(X_i-\overline{X})^2\) be 9.8 and 1.44, respectively. If the likelihood ratio test is used to test the hypothesis H0 : μ = 8.8 against H1 : μ > 8.8, then the p-value of the test equals __________ (round off to 3 decimal places)
Updated On: Oct 1, 2024
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Correct Answer: 0.017
Solution and Explanation
The correct answer is 0.017 to 0.021.(approx)
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