Question

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 30 waves showed an average wave height of x = 16.5 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.

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

  What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Estimate the P-value.

Sketch the sampling distribution and show the area corresponding to the P-value.

(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 α?

(e) Interpret your conclusion in the context of the application.

Answer 1

Solution:

(a) What is the level of significance?

Answer: The level of significance is 0.01

State the null and alternative hypotheses.

Answer:

(b) What sampling distribution will you use? Explain the rationale for your choice of the sampling distribution.

Answer: We should use the normal distribution because the sample is large and the population standard deviation is known.

  What is the value of the sample test statistic? (Round your answer to two decimal places.)

Answer: The test statistic is:

(c) Estimate the P-value.

Sketch the sampling distribution and show the area corresponding to the P-value.

(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 α?

We fail to reject the null hypothesis and the data is not statistically significant at 0.01 significance level

(e) Interpret your conclusion in the context of the application.

Answer: Since our p-value is > 0.01, we fail to reject the null hypothesis and there is not sufficient evidence to support the claim that that the storm is (perhaps temporarily) increasing above the severe rating