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 38 waves showed an average wave height of x = 17.3 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) State the null and alternate hypotheses. choose one: H0: ? < 16.4 ft; H1: ? = 16.4 ft H0: ? = 16.4 ft; H1: ? < 16.4 ft H0: ? > 16.4 ft; H1: ? = 16.4 ft H0: ? = 16.4 ft; H1: ? > 16.4 ft H0: ? = 16.4 ft; H1: ? ≠ 16.4 ft (b What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. choose one: The standard normal, since the sample size is large and ? is unknown. The Student's t, since the sample size is large and ? is unknown. The Student's t, since the sample size is large and ? is known. The standard normal, since the sample size is large and ? is known. c) What is the value of the sample test statistic? (Round your answer to two decimal places.)
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 38 waves showed an average wave height of x = 17.3 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) State the null and alternate hypotheses. choose one:
H0: ? < 16.4 ft; H1: ? = 16.4 ft
H0: ? = 16.4 ft; H1: ? < 16.4 ft
H0: ? > 16.4 ft; H1: ? = 16.4 ft
H0: ? = 16.4 ft; H1: ? > 16.4 ft
H0: ? = 16.4 ft; H1: ? ≠ 16.4 ft
(b What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. choose one:
The standard normal, since the
The Student's t, since the sample size is large and ? is unknown.
The Student's t, since the sample size is large and ? is known.
The standard normal, since the sample size is large and ? is known.
c) What is the value of the sample test statistic? (Round your answer to two decimal places.)
We have given that
Sample size n=38 , xbar = 17.3 , mu=16.4
Standard deviation sigma = 3.5
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