Answer
Step 1 : $H_0$: µ $\geq$ 59,593 dollars , $H_1$: µ < 59,593 dollars
Step 2: Since α = 0.01, and the test is a left-tailed test, the critical value is -2.33.
Step 3:
$\bar{X}$ = 58,800 dollars, µ =59,593 dollars, σ =1500 dollars, n = 30
Test value = z = $\frac{\bar{X}- µ }{σ / \sqrt n}$
= $\frac{58800 - 59593 }{1500 / \sqrt 30}$
= -2.896
Step 4 : Since the test value falls beyond the critical value, the decision is 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.
