Step 1 :The problem is asking for a hypothesis test to determine if the mean homicide rate in industrialized nations is different than the international average. This is a two-tailed test because we are looking for a difference in either direction (greater or less than).
Step 2 :The critical value is the z-score that corresponds to the desired level of statistical significance. In this case, the level of significance is 0.05.
Step 3 :To find the critical value, we need to find the z-score that corresponds to the 0.025 in each tail (since it's a two-tailed test and we split the level of significance in half for each tail).
Step 4 :The critical value is approximately 1.96. However, since we are conducting a two-tailed test, the critical value will be both positive and negative.
Step 5 :Final Answer: The critical values are \(\boxed{-1.96 / 1.96}\).