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 39 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.

Answer 1

pvalue = 0.4286 > 0.01, so this information does not suggest that the storm is (perhaps temporarily) increasing above the severe rating

Explanation:

The null hypothesis is:

`H_(0) = 16.4`

The alternate hypotesis is:

`H_(1) > 16.4`

Our test statistic is:

In which X is the statistic,
`\mu` is the mean,
`\sigma` is the standard deviation and n is the size of the sample.

In this problem, we have that:

`\mu = 16.4, \sigma = 3.5, X = 16.5, n = 39`

So

`t = (16.5 - 16.4)/((3.5)/(√(39)))`

`t = 0.18`

Looking at the z-table, z = t = 0.18 has a pvalue of 0.5714.

The alternate hypothesis is accepted if there is a lower than 1%(Because of α = 0.01) probability of finding a value higher than X.

In this problem, X = 16.5, with a pvalue of 0.5714.

1 - 0.5714 = 0.4286 > 0.01

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