Question 1110954: 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 = 17.1 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?
State the null and alternate hypotheses.
H0: μ = 16.4 ft; H1: μ ≠ 16.4 ft
H0: μ = 16.4 ft; H1: μ > 16.4 ft
H0: μ > 16.4 ft; H1: μ = 16.4 ft
H0: μ < 16.4 ft; H1: μ = 16.4 ft
H0: μ = 16.4 ft; H1: μ < 16.4 ft
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since the sample size is large and σ is known.
The Student's t, since the sample size is large and σ is unknown.
The standard normal, since the sample size is large and σ is unknown.
The Student's t, since the sample size is large and σ is known.
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 by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! (a) level of significance is 1%
:
The null and alternative hypotheses are H0: μ = 16.4 ft; H1: μ > 16.4 ft
:
(b) Use the standard normal, since the sample size is large and σ is known
:
Note σ is the standard deviation of the population
:
Here n=34, which has a square root of 5.831 so the standard error is 3.5/5.831 = 0.6002.
:
Our test statistic is z = (17.1 - 16.4)/0.6002 = 1.1663
:
Using z-tables the probability associated with 1.1663 is 0.8783, this is our p-value
:
since our p-value is > 0.01, we accept the null hypothesis which is that the storm is not increasing above the severe rating
:
|
|
|
