In: Statistics and Probability
Determine the uniformly most powerful test of H0:θ≤1 versus H1:θ >1 for a random sample of 25 from N(0,θ), at the significance level α=.05.
To determine the UMP test firstly find the best critical region according to the test hypothesis given in the question .after that you will able to find the most powerful (MP) region (w) with the help of the neyman and pearson lemma.now you can find size of the test ,power of the test and so which is required in question .