Question: can anyone help with this pleaseeee 2. X - (X,, X2,..., X. ) is a random sample from a N (0,o?) population, with known mean

can anyone help with this pleaseeee

2. X - (X,, X2,..., X. ) is a random sample from a N (0,o?) population, with known mean 0 and unknown variance of . It is desired to test the hypotheses: VS H : 0' > o. (i) Derive the Neyman-Pearson (NP) test of these hypotheses, detailing your chosen method. [7] (ii) Determine the level a =.05 test of these hypotheses. You are given that when X,, X,,..., X,, are i.i.d. N (H.G' ) then ).[ -# ) - x2. [5] (iii) A random sample of 20 readings to measure the precision of a new instrument gave X? = 15 . 1=1 Test the hypotheses Ho :o' =1 vs H, :o' > 1 at level .05. [4] (iv) It is desired to find a (1-)100% confidence interval for of when u is known. Given that P( Xian, X, SXaza)=1-a, determine the corresponding confidence interval for o' [5]

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