Given
[tex]\begin{gathered} H_0\colon p=0.61 \\ H_1\colon p<0.61 \end{gathered}[/tex]
The test statistics formula for proportion is given by
[tex]z=\frac{p-p_0}{\sqrt[]{\frac{p_0(1-p_0)}{n}}}[/tex]
The parameters are
[tex]\begin{gathered} p=\frac{61}{97}=0.6289 \\ p_0=0.61 \\ n=97 \end{gathered}[/tex]
using the formula
[tex]\begin{gathered} z=\frac{0.6289-0.61}{\sqrt[]{\frac{0.61(1-0.61)}{97}}} \\ z=\frac{0.0189}{\sqrt[]{0.002453}} \\ z=0.3816 \end{gathered}[/tex]
Thus, the test statistics to 3 decimal place is 0.382
