X1, ... , Xn is an i.i.d. sample from N(0,02), where both 0 E R and o2 > 0 are unknown. Sample size n = 25, the value of

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X1 Xn Is An I I D Sample From N 0 02 Where Both 0 E R And O2 0 Are Unknown Sample Size N 25 The Value Of 1 (59.84 KiB) Viewed 106 times

X1, ... , Xn is an i.i.d. sample from N(0,02), where both 0 E R and o2 > 0 are unknown. Sample size n = 25, the value of the sample mean X is = X = =n ΣX = - X; = 0.8, 52 = (n − 1)-'__, (X; – X)? = 2.56. 2 i=1 i=1 : : Consider hypotheses Ho : 0 = 0 vs H1:0 > 0 (a) (2 points) Let a = 0.05. Construct a test for testing Ho against H at significance level a, using Student's Theorem. (b) (1 point) Find power function for the constructed test.