Weatherwise is a magazine published by the American Meteorological Society. One

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 = 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

= 17.4 feet. Previous studies of severe storms indicate that = 4.0 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use = 0.01. Solve the problem using the critical region method of testing (i.e., traditional method).

what is the t statistc and the critical value

Explanation / Answer

here as it is right tailed test and we know population std deviation

at 0.01 level critical value of z=2.326

for std error =std deviaiton/(n)1/2 =0.7303

hence test stat z=(X-mean)/std error =(17.4-16.4)/0.7303=1.369

as test stat is not higher then critical value we can not reject null hypothesis.

And can not conclude that  the storm is (perhaps temporarily) increasing above the severe rating

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