Question

Let Y_(1),...,Y_(n) be a random sample from a distribution with the density function f_(\theta )(y)=(3\theta ^(3))/(y^(4)),y>=\theta >0 (a) Find a UMP test of H_(0):\theta <=\theta _(0) vs. H_(1):\theta >\theta _(0) (b) Consider the special case H_(0):\theta <=1 vs. H_(1):\theta >1. Take the sample size be n=5. Determine the decision rule that with the probability of type I error P(Reject H_(0)|\theta =1. Then determine the probability P(Reject H_(0)|\theta =2. (c) Following part (b), create a plot of the power function. Determine the range of values for the parameter \theta that result in a power function exceeding 0.9 (Specify values up to 4 decimal places for precision).

          Let Y_(1),...,Y_(n) be a random sample from a distribution with the density
function
f_(\theta )(y)=(3\theta ^(3))/(y^(4)),y>=\theta >0
(a) Find a UMP test of H_(0):\theta <=\theta _(0) vs. H_(1):\theta >\theta _(0)
(b) Consider the special case H_(0):\theta <=1 vs. H_(1):\theta >1. Take the
sample size be n=5. Determine the decision rule that with the probability of type I error  P(Reject H_(0)|\theta =1. Then determine the probability P(Reject H_(0)|\theta =2.
(c) Following part (b), create a plot of the power function. Determine the range of values for the parameter \theta  that result in a power function exceeding 0.9 (Specify values up to 4 decimal places for precision).

Added by Christopher C.

Question

Please give Ace some feedback