Answer
No. Yes. See explanations.
Work Step by Step
Given $\mu=35, \sigma= 3, n=36, \bar X=33.5$
a. State the hypotheses and identify the claim.
$H_o: \mu=35$
$H_a: \mu\ne 35$ (claim, two tail test)
b. Find the critical value(s).
$\alpha/2=0.05, |z_c|=1.645$
c. Compute the test value.
$z=\frac{33.5-35}{3/\sqrt {36}}=-3$
d. Make the decision.
Since $z\lt-1.645$, we should reject the null hypothesis.
e. Summarize the results.
At α= 0.10. the tires are not properly inflated.
For $c=0.6$, we have $z_c=1.645$ and the margin of error is
$E=1.645\times\frac{3}{\sqrt {36}}=0.82$ and the interval is
$(33.5-0.82, 33.5+0.82)$ which gives $32.7\leq \mu \leq 34.3$
and clearly the mean $\mu=35$ is outside the range and we should
reject the null hypothesis. The results from the two calculations agree with each other.
