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10 July, 18:03

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 33 waves showed an average wave height of x = 17.1 feet. Previous studies of severe storms indicate that σ = 3.9 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01. Solve the problem using the critical region method of testing (i. e., traditional method). (Round your answers to two decimal places.)

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  1. 10 July, 19:22
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    Step-by-step explanation:

    We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

    For the null hypothesis,

    µ = 16.4

    For the alternative hypothesis,

    µ ≠ 16.4

    This is a 2 tailed test

    Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

    z = (x - µ) / (σ/√n)

    Where

    x = sample mean

    µ = population mean

    σ = population standard deviation

    n = number of samples

    From the information given,

    µ = 16.4

    x = 17.1

    σ = 3.1 feet

    n = 31

    z = (17.1 - 16.4) / (3.1/√31) = 0.89

    The calculated test statistic is 0.89 for the right tail and - 0.89 for the left tail

    Since α = 0.01, the critical value is determined from the normal distribution table.

    For the left, α/2 = 0.01/2 = 0.005

    The z score for an area to the left of 0.005 is - 2.575

    For the right, α/2 = 1 - 0.005 = 0.995

    The z score for an area to the right of 0.995 is 2.575

    In order to reject the null hypothesis, the test statistic must be smaller than - 2.575 or greater than 2.575

    Since - 0.89 > - 2.575 and 0.89 < 2.575, we would fail to reject the null hypothesis.

    Therefore, this information does not suggest that the storm is (perhaps temporarily) increasing above the severe rating
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