Chapter 6.4, Problem 10Q

Suppose a sample of size 1 is taken from the pdf $f_Y\left(y\right)=\left(1\text{/}\lambda \right)e^{-y/\lambda },y>0$, for the purpose of testing

$H_0:\lambda =1$

versus

$H_1:\lambda >1$

The null hypothesis will be rejected if $y\ge 3.20$.

• (a) Calculate the probability of committing a Type I error.

• (b) Calculate the probability of committing a Type II error when $\lambda =\frac{4}{3}$.

• (c) Draw a diagram that shows the $\alpha$ and $\beta$ calculated in parts (a) and (b) as areas.