Weatherwise is a magazine published by the American Meteorological Society.

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 31 waves showed an average wave height of x = 16.9 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 is the level of significance? State the null and alternate hypotheses. H0: μ > 16.4 ft; H1: μ = 16.4 ft H0: μ < 16.4 ft; H1: μ = 16.4 ft H0: μ = 16.4 ft; H1: μ ≠ 16.4 ft H0: μ = 16.4 ft; H1: μ < 16.4 ft H0: μ = 16.4 ft; H1: μ > 16.4 ft

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student’s t, since the sample size is large and σ is unknown. The standard normal, since the sample size is large and σ is known. The Student’s t, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ is unknown. What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Estimate the P-value. P-value > 0.250 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010

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