In: Statistics and Probability
Weatherwise is a magazine published by the American
Meteorological Society. One issue gives a rating system used to
classify Nor'easter storms that frequently hit New England and can
cause much damage near the ocean. A severe storm has an average
peak wave height of μ = 16.4 feet for waves hitting the
shore. Suppose that a Nor'easter is in progress at the severe storm
class rating. Peak wave heights are usually measured from land
(using binoculars) off fixed cement piers. Suppose that a reading
of 39 waves showed an average wave height of x = 17.3
feet. Previous studies of severe storms indicate that σ =
3.5 feet. Does this information suggest that the storm is (perhaps
temporarily) increasing above the severe rating? Use α =
0.01.
a.) What are the null and alternate hypotheses?
b.) What is the value of the sample test statistic? (Round your answer to two decimal places.)
c.) Estimate the P-value.
d.) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?