A researcher compares the average math scores of $55$ randomly selected sophomore students and $60$ randomly selected junior students. The mean score for sophomores is $88$, with a population standard deviation of $12$. The mean score for juniors is $91$, with a population standard deviation of $15$. The claim is that the mean score for sophomores is greater than the mean score for juniors. Should the hypothesis test be left-tailed, right-tailed, or two-tailed, and should a $z$-test or $t$-test be used?

• A. Right-tailed $z$-test
• B. Left-tailed $t$-test
• C. Two-tailed $t$-test
• D. Left-tailed $z$-test

Answer: (A)