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 34 waves showed an average wave height of x = 17.5 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.
(a) What is the level of significance? ____________________________
(b) What is the value of the sample test statistic? (Round your answer to two decimal places.) ______________
(c) Find the P-value. (Round your answer to four decimal places.) ___________________
Solution :
This is the right tailed test .
The null and alternative hypothesis is ,
H0 : = 16.4
Ha : > 16.4
= 17.5
= 16.4
= 3.5
n = 34
(a) level of significance = 0.01
(b)
Test statistic = z
= ( - ) / / n
= (17.5 - 16.4) /3.5 / 34
= 1.83
Test statistic = 1.83
(c)
P(z > 1.83) = 1 - P(z < 1.83) = 1 - 0.9664 = 0.0336
P-value = 0.0336
= 0.01
P-value >
Fail to reject the null hypothesis .
There is no evidence to suggest that the storm is (perhaps temporarily) increasing above the severe rating .
Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system...
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....
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....
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....
is a magazine published by the 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 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 w 16.4 feet...
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