Answer Happy

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 = 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. Ho: μ = 16.4 ft; H₁: μ = 16.4 ft O Ho: μ> 16.4 ft; H₁: μ = 16.4 ft O Ho: μ< 16.4 ft; H₁: μ = O Ho: μ = 16.4 ft; H₁: μ > 16.4 ft O Ho: μ = 16.4 ft; H₁: μ< 16.4 ft 16.4 ft (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and o is known. O The Student's t, since the sample size is large and σ is known. O The standard normal, since the sample size is large and σ is unknown. O The Student's t, 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. O P-value > 0.250 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O P-value < 0.010
Sketch the sampling distribution and show the area corresponding to the P-value. 0-3 - 2 -2 -1 -1 0 0 1 1 2 2 3 3 O-3 -2 -2 -1 -1 0 0 1 1 2 (e) Interpret your conclusion in the context of the application. O There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating. O There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating. 2 3 0-3 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. 3