Step 1 :The problem is asking for the value of the test statistic in a hypothesis test for a proportion. The test statistic in this case is a z-score, which is calculated as \( (p̂ - p0) / \sqrt{(p0 * (1 - p0)) / n} \), where \( p̂ \) is the sample proportion, \( p0 \) is the population proportion under the null hypothesis, and \( n \) is the sample size. In this case, \( p̂ = 0.42 \), \( p0 = 0.38 \), and \( n = 350 \).
Step 2 :Substitute the given values into the formula: \( z = (0.42 - 0.38) / \sqrt{(0.38 * (1 - 0.38)) / 350} \)
Step 3 :Calculate the z-score to get the test statistic for the hypothesis test.
Step 4 :The calculated z-score is 1.54.
Step 5 :Final Answer: The value of the test statistic is \( \boxed{1.54} \).