Step 1 :We are given the following values: sample mean (\(\bar{X}\)) is \$48,061, population mean (\(\mu\)) is \$47,500, standard deviation (\(\sigma\)) is \$2,351, and sample size (\(n\)) is 86.
Step 2 :We are asked to find the test statistic (\(Z\)) used in a hypothesis test. The formula for the test statistic in a hypothesis test for a population mean is \(Z = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}}\).
Step 3 :Substitute the given values into the formula: \(Z = \frac{48061 - 47500}{2351 / \sqrt{86}}\).
Step 4 :Solving the above expression, we find that \(Z = 2.213\).
Step 5 :Final Answer: The value of the test statistic used in the hypothesis test is \(\boxed{2.213}\).