Answer
a)two-tailed
b)student t-distribution
Work Step by Step
a) The alternative hypothesis is: $\mu\ne0$. If the alternative hypothesis contains $\ne$ then the test is two-tailed. If the alternative hypothesis contains < then the test is left-tailed. If the alternative hypothesis contains > then the test is right-tailed. Hence it is two-tailed.
b) Here we have a hypothesis test involving the mean but we do not know the standard deviation, hence the student t-distribution is used.
