Step 1 :The question is asking for the alternative hypothesis in a hypothesis test where we are comparing the mean homicide rate in industrialized nations to the international average. The null hypothesis in this case would be that the mean homicide rate in industrialized nations is equal to the international average. The alternative hypothesis is what we would believe if the null hypothesis is rejected. In this case, the alternative hypothesis would be that the mean homicide rate in industrialized nations is not equal to the international average. Therefore, the alternative hypothesis is \(\mathrm{H}_{1:} \mu \neq 2.92\).
Step 2 :Final Answer: \(\boxed{\mathrm{H}_{1:} \mu \neq 2.92}\)