Question 13.2: Wave Heights An oceanographer wishes to test the claim that ......
Wave Heights
An oceanographer wishes to test the claim that the median height of waves in a resort town on the Atlantic Ocean is 2.4 feet. A random sample of 50 days shows the heights of the waves on 20 days were at least 2.4 feet. At α = 0.05, test the claim that the median height of the waves is at least 2.4 feet.
Step 1 State the hypotheses and identify the claim.
H_{0}: \mathrm{MD}=2.4 \text { and } H_{1}: \mathrm{MD}<2.4
Step 2 Find the critical value. Since \alpha=0.05 and n=50, and since the test is left-tailed, the critical value is -1.65, obtained from Table E.
Step 3 Compute the test value.
z=\frac{(x+0.5)-0.5 n}{\sqrt{n} / 2}=\frac{(20+0.5)-0.5(50)}{\sqrt{50} / 2}=\frac{-4.5}{3.536}=-1.27
Step 4 Make the decision. Since the test value of -1.27 is greater than -1.65, the decision is to not reject the null hypothesis.
Step 5 Summarize the results. There is not enough evidence to reject the claim that the median height of the waves is at least 2.4 feet.