Chapter 10.10, Problem 102E

a.

To determine

Verify that $\frac{L\left(p_0\right)}{L\left(p_a\right)}={\left[\frac{p_0\left(1-p_a\right)}{\left(1-p_0\right)p_a}\right]}^{{\displaystyle \sum y_i}}{\left(\frac{1-p_0}{1-p_a}\right)}^n$.

Prove that $\frac{L\left(p_0\right)}{L\left(p_a\right)}<k$ if and only if ${\displaystyle \sum _{i=1}^n{y}_i}>k^{*}$ for some constant $k^{\text{'}}$.

Provide the rejection region for the most powerful test of $H_0\text{ versus }{H}_a$.

b.

To determine

The values of constants contained in the rejection region derived in Part (a [iii]).

c.

To determine

State whether the test given in Part (a) is uniformly most powerful for $H_0:p=p_0$ versus $H_a:p>p_0$.