#### Answer

Yes, see explanations.

#### Work Step by Step

Given $p=0.205, n=120, \hat p=38/120=0.317$
a. State the hypotheses and identify the claim.
$H_o: p\leq 0.205$
$H_a: p\gt 0.205$ (claim, right tail test)
b. Find the critical value(s).
$\alpha=0.10, z_c=1.28, E=1.28\times\sqrt {\frac{0.317\times0.683}{120}}=0.054$
c. Compute the test value.
$z=\frac{0.317-0.205}{\sqrt {0.205\times0.795/120}}=3.04$
The confidence interval is $(0.317-0.054, 0.317+0.054)$ which gives $0.263\leq p\leq 0.371$
d. Make the decision.
Confidence interval test: the range of predicted proportion is larger than 0.205 which confirms the claim.
Hypothesis test: $z\gt z_c$ we have enough evidence to reject the null hypothesis and support the claim.
e. Summarize the results.
We used both confidence interval and hypothesis tests and conclude that at $\alpha=0.1$, the proportion is greater than $20.5\%$