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 fi xed cement piers. Suppose that a reading of 36 waves showed an average wave height of x 5 17.3 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 a=0.01.

Answer 1

given that population mean(mu) = 16.4 and sample mean (x bar) = 17.3

population standard deviation (sigma) = 3.5

sample size is n =36

Null hypothesis Ho:- mu = 16.4

Alternate hypothesis Ha:- mu >16.4

test statistic = (xbar - mu)/(sigma/sqrt(n))

setting the given values, we get

= (17.3-16.4)/(3.5/sqrt(36))

= 0.9/0.5833

= 1.54

test statistic is z = 1.54

using z table, find 1.5 in the left most column and 0.04 in the top row, then select the intersecting cell, we get

p value = 0.0618

p value is greater than significance level of 0.01, we failed to reject the null hypothesis

Therefore, we can say that at 0.01 significance level, there is insufficient evidence to conclude that the storm is increasing above the severe rating