ANSWER
Z = -1.25
EXPLANATION
Given:
[tex]Hypotheses=\begin{cases}{H_0:p\text{ = 0.25}} \\ {H_a:p<0.25} \\ {}\end{cases}[/tex]Desired Outcome:
Test Statistic z
Determine the Test Statistic z
[tex]z\text{ = }\frac{p\text{ - p}_0}{\sqrt{\frac{p_0(1\text{ - p}_0)}{n}}}[/tex][tex]\begin{gathered} z\text{ = }\frac{0.20-0.25}{\sqrt{\frac{0.25(1\text{ - 0.25\rparen}}{100}}} \\ z\text{ = }\frac{-0.05}{\sqrt{\frac{0.1875}{100}}} \\ z\text{ = }\frac{-0.05}{0.04} \\ z\text{ = -1.25} \end{gathered}[/tex]