MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**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 \(\mu = 16.4\) 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 36 waves showed an average wave height of \(\bar{x} = 16.9\) feet. Previous studies of severe storms indicate that \(\sigma = 3.5\) feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use \(\alpha = 0.01\).

### (a) What is the level of significance?
State the null and alternate hypotheses:

- \( H_0: \mu = 16.4 \text{ ft}; \; H_1: \mu > 16.4 \text{ ft} \)
- \( H_0: \mu < 16.4 \text{ ft}; \; H_1: \mu = 16.4 \text{ ft} \)
- \( H_0: \mu = 16.4 \text{ ft}; \; H_1: \mu < 16.4 \text{ ft} \)
- \( H_0: \mu = 16.4 \text{ ft}; \; H_1: \mu \neq 16.4 \text{ ft} \)
- \( H_0: \mu > 16.4 \text{ ft}; \; H_1: \mu = 16.4 \text{ ft} \)

### (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
- \( \text{The standard normal, since the sample size is large and }\sigma \text{ is known.} \)
- \( \text{The Student's } t, \text{ since the sample size is large and }\sigma \text{ is known.} \)
- \( \text{The standard normal, since the sample size is large and }\sigma \text{ is unknown.} \)
- \( \text
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Transcribed Image Text:**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 \(\mu = 16.4\) 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 36 waves showed an average wave height of \(\bar{x} = 16.9\) feet. Previous studies of severe storms indicate that \(\sigma = 3.5\) feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use \(\alpha = 0.01\). ### (a) What is the level of significance? State the null and alternate hypotheses: - \( H_0: \mu = 16.4 \text{ ft}; \; H_1: \mu > 16.4 \text{ ft} \) - \( H_0: \mu < 16.4 \text{ ft}; \; H_1: \mu = 16.4 \text{ ft} \) - \( H_0: \mu = 16.4 \text{ ft}; \; H_1: \mu < 16.4 \text{ ft} \) - \( H_0: \mu = 16.4 \text{ ft}; \; H_1: \mu \neq 16.4 \text{ ft} \) - \( H_0: \mu > 16.4 \text{ ft}; \; H_1: \mu = 16.4 \text{ ft} \) ### (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. - \( \text{The standard normal, since the sample size is large and }\sigma \text{ is known.} \) - \( \text{The Student's } t, \text{ since the sample size is large and }\sigma \text{ is known.} \) - \( \text{The standard normal, since the sample size is large and }\sigma \text{ is unknown.} \) - \( \text
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