Weatherwise is a magazine published by the American Meteorol

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 40 waves showed an average wave height of x = 17.1 feet. Previous studies of severe storms indicate that = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use = 0.01.

(a) What is the level of significance?
I would say it\'s 0.01

(b)What is the value of the sample test statistic? (Round your answer to two decimal places.)
How do I calculate this?


(c) Find the P-value. (Round your answer to four decimal places.)

I don\'t understand how to find the p-value.

Solution

a)

Yes, it is 0.01, as given. [answer]

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b)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   16.4  
Ha:    u   >   16.4  
              
As we can see, this is a    right   tailed test.      
                              
Getting the test statistic, as              
              
X = sample mean =    17.1          
uo = hypothesized mean =    16.4          
n = sample size =    40          
s = standard deviation =    3.5          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.264911064   [ANSWER]

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Also, the p value is, getting the right tailed area of the z score above using table/technology,              
              
p =    0.102951605   [ANSWER]

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[You can use a technology like Excel or a ti-84 calculator to get the right tailed area of a z score. That is the P value here.]