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 30 waves showed an average wave height of x = 17.0 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? 0.01

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.)

???

Answer 1

Solution :

= 16.4

= 17.0

= 3.5

n = 30

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 16.4

H_a : > 16.4

Test statistic = z

= ( - ) / / n

= (17.0- 16.4) /3.5 / 30

= 0.939 = 0.94

p(Z > 0.94 ) = 1-P (Z < 0.94 ) = 0.1739

P-value = 0.1739

= 0.01  

p= 0.1739 ≥ 0.01

Fail to reject the null hypothesis.