Answer
Yes, see explanations.
Work Step by Step
Given $p=0.602, n=400, \hat p=260/400=0.65$
a. State the hypotheses and identify the claim.
$H_o: \mu\leq 0.602$
$H_a: \mu\gt 0.602$ (claim, right tail test)
b. Find the critical value(s).
With $\alpha=0.05, z_c=1.645$
c. Compute the test value.
$z=\frac{0.65-0.602}{\sqrt {0.602\times0.398/400}}=1.96$
d. Make the decision.
Since $z\gt z_c$, we have enough evidence to reject the null hypothesis and support the claim.
e. Summarize the results.
At $\alpha=0.05$, the warden is right that in his prison the percentage is even higher.