Step 1 :Given that the sample mean \(\bar{X} = 67.7\), the population mean \(\mu = 69\), the standard deviation \(\sigma = 10.9\), and the sample size \(n = 149\).
Step 2 :The test statistic for a hypothesis test about a population mean can be calculated using the formula: \[Z = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}}\]
Step 3 :Substitute the given values into the formula: \[Z = \frac{67.7 - 69}{10.9 / \sqrt{149}}\]
Step 4 :Solving the above expression gives the value of the test statistic as approximately -1.46.
Step 5 :\(\boxed{\text{Final Answer: The value of the test statistic is approximately -1.46.}}\)