hypothesis testing practice question

hypothesis testing practice question

This is a practice question for a final exam.
Two types of cordless weed-trimmer batteries are tested. One group of 5
batteries averaged $1.4$ hours, while the other group consisting of 8
batteries, averaged $1.2$ hours.
A) What null and alternative hypotheses would you establish to determine
whether or not the battery life differs between the two types?
ANS: I think the answer to this is
$H_0: \mu_1 = \mu_2$
$H_1: \mu_1 \neq \mu_2$
B) What test statistic is appropriate if
${ó_1}^2 = 6.7$ $ {ó_2}^2$ = 5.2. (Please print out the appropriate formula.)
Ans: I think it is Z distribution. I have no idea why its just an
intuition that it may be Z distribution. Could use some help or advice on
how to identify the distribution.
C) Construct the appropriate critical values, assuming $á =0.05$. Would
you accept the null or the alternative hypothesis?
Ans. Definitely need help here. Completely lost.
D) What p-value would you report if á is not specified?