Answer
Step 1 : $H_0$: µ = 305 feet, $H_1$: µ $\gt$ 305 feet
Step 2: Since α = 1-0.05=0.95, and the test is a right-tailed test, the critical values are 1.645.
Step 3:
$\bar{X}$ = 306.2 feet , µ = 305 feet , σ = $\sqrt 3.6 $ = 1.8974 , n = 55
Test value = z = $\frac{\bar{X}- µ }{σ / \sqrt n}$
= $\frac{306.2- 305 }{1.8974 / \sqrt 55}$
= 4.69
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 average depth has increased at the 0.05 level of significance.
