#### Answer

Yes, see explanations.

#### Work Step by Step

We are given $n1=20, \bar X1=172/20=8.6, s1=3.6$ and $n2=30, \bar X2=366/30=12.2, s2=4.2$
a. State the hypotheses and identify the claim.
$H_o: \mu1-\mu2=0$
$H_a: \mu1-\mu2 \ne 0$ (claim, two tail test)
b. Find the critical value(s).
$\alpha/2=0.005, df=19, |t_c|=2.861$
c. Compute the test value.
$z=\frac{8.6-12.2-0}{\sqrt {\frac{3.6^2}{20}+\frac{4.2^2}{30}}}=-3.24$
d. Make the decision.
Since $z\lt -2.861$, we reject the null hypothesis.
e. Summarize the results.
At α= 0.01, a difference in means can be concluded.