Answer
Yes, see explanations.
Work Step by Step
a. State the hypotheses and identify the claim.
$H_o: \mu_D=0$
$H_a: \mu_D\gt0$ (claim, right tail test)
b. Find the critical value(s).
$\alpha=0.05, df=5, t_c=2.015$
c. Compute the test value.
$n=6, \sum D=61, \bar D=10.2, \sum D^2=659,$
$S_D=\sqrt {\frac{6\times659-61^2}{6\times5}}=7.77, t=\frac{10.2-0}{7.77/\sqrt 6}=3.22$
d. Make the decision.
As $t>t_c$, we reject the null hypothesis.
e. Summarize the results.
At $\alpha=$ 0.05, there is sufficient evidence that the scores improved.