Answer
Step 1 : $H_0$: µ $\leq$ 8121 dollars , $H_1$: µ > 8121 dollars
Step 2: Since α = 1-0.01=0.99, and the test is a right-tailed test, the critical value is 2.33.
Step 3:
$\bar{X}$ = 152.59 dollars, µ =150 dollars, σ =10.78 dollars, n = 38
Test value = z = $\frac{\bar{X}- µ }{σ / \sqrt n}$
= $\frac{152.59- 150}{10.78 / \sqrt 38}$
=1.48
Step 4 : Since the test value falls within the critical value, the decision is not to reject the null hypothesis.
Step 5: There is enough evidence to support the claim that the state employees earn on average less than federal employees.
