Answered: What sampling distribution will you…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 ? = 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 32 waves showed an average wave height of x = 16.5 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) What is the level of significance?=___

State the null and alternate hypotheses.

A-H₀: ? = 16.4 ft; H₁: ? ≠ 16.4 ft

B-H₀: ? > 16.4 ft; H₁: ? = 16.4 ft

C-H₀: ? = 16.4 ft; H₁: ? < 16.4 ft

D-H₀: ? < 16.4 ft; H₁: ? = 16.4 ft

E-H₀: ? = 16.4 ft; H₁: ? > 16.4 ft

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

A-The Student's t, since the sample size is large and ? is unknown.

B-The standard normal, since the sample size is large and ? is known.

C-The Student's t, since the sample size is large and ? is known.

D-The standard normal, since the sample size is large and ? is unknown.

What is the value of the sample test statistic? (Round your answer to two decimal places.)=__

A-P-value > 0.250

B-0.100 < P-value < 0.250

C-0.050 < P-value < 0.100

D-0.010 < P-value < 0.050

E-P-value < 0.010

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

A-At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

B-At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

C-At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

D-At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

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