Step 1 :Given that the population mean (\(\mu\)) is 13, the population standard deviation (\(\sigma\)) is 6.5, and the sample size (\(n\)) is 32. The sample data is [9.4, 13.8, 10.2, 20.6, 18.2, 21.1, 16.7, 21.8, 7.1, 20.1, 22.1, 9.1, 13.9, 21.6, 15.6, 13.4, 15.8, 20.1, 12.8, 9.3, 9.6, 8.4, 12.4, 9.1, 20.9, 20.9, 19.5, 7.9, 7.6, 21.5, 8.3, 20.6].
Step 2 :Calculate the sample mean (\(\bar{x}\)) from the given data. The sample mean is 14.98125.
Step 3 :Substitute all the values into the z-score formula to calculate the standardized test statistic. The formula for the z-score is \(z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}\).
Step 4 :Substitute \(\bar{x} = 14.98125\), \(\mu = 13\), \(\sigma = 6.5\), and \(n = 32\) into the formula to get \(z = 1.7242526895087347\).
Step 5 :Round the standardized test statistic to two decimal places. The final answer is \(\boxed{1.72}\).