Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Tests of Hypotheses
Let X1, X2 be a random sample from a population having probability density function f ∈ { f0, f1} where
\(\rm f_0(x)=\left\{\begin{matrix}\frac{1}{2}& if\ 0\le x\le 2\\\ 0&otherwise\end{matrix}\right.\ and \ \rm f_1(x)=\left\{\begin{matrix}\frac{1}{4}& if\ 0\le x\le 4\\\ 0&otherwise\end{matrix}\right.\)
For testing the null hypothesis H0 : f = f0 against the alternate hypothesis H1 : f = f1, the power of a most powerful test of size α = 0.05 is equal to
1
0.4625
2
0.5425
3
0.7625
4
0.6225