Evaluate \( z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \) if \( \bar{x}=5.3, \mu=37.8, \sigma=6.9 \), and \( n=16 \). \( \begin{array}{l}z=\square \\ \text { (Type an integer or decimal rounded to two decimal places as needed.) }\end{array} \)

To evaluate \( z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \), we first need to substitute the given values into the formula. Given: - \( \bar{x} = 5.3 \) - \( \mu = 37.8 \) - \( \sigma = 6.9 \) - \( n = 16 \) Now, we compute \( \frac{\sigma}{\sqrt{n}} \): \[ \frac{\sigma}{\sqrt{n}} = \frac{6.9}{\sqrt{16}} = \frac{6.9}{4} = 1.725. \] Next, we can substitute these values into the \( z \) formula: \[ z = \frac{5.3 - 37.8}{1.725} = \frac{-32.5}{1.725} \approx -18.88. \] Therefore, the final evaluated result is: \[ z \approx -18.88. \]