Statistics Question. Problem A manufacturer of hard safety hats for construction workers is concerned about the variation of the forces its helmets transmit to wearers when subjected to an external force. For simplicity, we assume that the measurements of the forces of n helmets in an experiment that transmit to wearers, X1, …, Xn, are a random sample from N(0, σ2 ) where σ 2 is unknown. Consider testing H0 : σ 2 = σ 2 0 vs. H1 : σ 2 = σ 2 1 where the known constants satisfy σ 2 0 < σ2 1 .

3.1 Apply likelihood ratio test (LRT) to show that we reject H0 if Pn i=1 X2 i > c for some constant c.

3.2 Find the value of c to make it a level α test.

3.3 Find a (1 − α)100% confidence interval of σ 2 using the LRT found in 3.2. 3.4 Suppose H0 : σ 2 = 1 vs. H1 : σ 2 = 4, sample size n = 10 and α = 0.05. Find the value of c and the power of the LRT.

After solving the questions please also provide answers doing computational method using R programming and show both methods (computational and scientific)

Statistics Question

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