Step 1 :Given the claim is that \(\mu>1220\). The null hypothesis, \(H_{0}\), is the statement that the mean is less than or equal to 1220, and the alternative hypothesis, \(H_{a}\), is the statement that the mean is greater than 1220.
Step 2 :We are given the sample mean, \(\bar{x}=1243.48\), the sample size, \(n=300\), and the population standard deviation, \(\sigma=195.94\).
Step 3 :We can use these values to calculate the standardized test statistic, which is a z-score. The formula for the z-score is \(z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}\)
Step 4 :Substitute the given values into the formula to find the z-score: \(\mu = 1220\), \(\bar{x} = 1243.48\), \(n = 300\), \(\sigma = 195.94\)
Step 5 :The calculated z-score is approximately 2.08. This is the standardized test statistic that we were asked to find.
Step 6 :Final Answer: The standardized test statistic is approximately \(\boxed{2.08}\)