Weatherwise magazine is published in association with the American Meteorological Society. Volume 46, Number 6, has a rating system to classify nor’easter storms that frequently hit New England states and can cause much damage near the ocean coast. A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a nor’easter is in progress at the severe storm class rating.
(a) Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. What would be the null hypothesis regarding average wave height?
(b) If you wanted to test the hypothesis that the storm is getting worse, what would you use for the alternate hypothesis?
(c) If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis?
(d) Suppose you do not know whether the storm is getting worse or dying out. You just want to test the hypothesis that the average wave height is different from (either higher or lower than) from the severe storm class rating. What would you use for the alternate hypothesis?
(e) For each of the tests in parts (b)–(d), would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean? Explain your answer in each case.