Answer
Step 1 : $H_0$: µ = 30.9 hours, $H_1$: µ $\ne$ 30.9 hours
Step 2: Since α = 0.01/2 = 0.005, and the test is a two-tailed test, the critical values are -2.575 and +2.575.
Step 3:
$\bar{X}$ = 32.1 hours , µ = 30.9 hours, σ = 3.6, n = 32
Test value = z = $\frac{\bar{X}- µ }{σ / \sqrt n}$
= $\frac{32.1 - 30.9 }{3.6 / \sqrt 32}$
= 1.886
Step 4 : Since the test value falls within the critical value, the decision is not to reject the null hypothesis.
Step 5: There is not enough evidence to support the claim that at the 0.01 level of significance, the sample mean differs from the national mean.
