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 ? = 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 37 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.
O H: = 16.4 t; H,:< 16.4 ft
O H: = 16.4 t; H: = 16.4 ft
O H: H = 16.4 ft; H,: > 16.4 ft
O Ho: A> 16.4 ft; H: = 16.4 ft
OH: H< 16.4 ft; H,: = 16.4 ft
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The standard normal, since the sample size is large and o is unknown.
O The standard normal, since the sample size is large and o is known.
O The Student's t, since the sample size is large and o is unknown.
O The Student's t, since the sample size is large and o is known.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Estimate the P-value.
O P-value > 0.250
O 0.100 < P-value < 0.250
O 0.050 < P-value < 0.100
O 0.010 < P-value < 0.050
O P-value < 0.010
Sketch the sampling distribution and show the area corresponding to the P-value.
o-3
-1
-2
-2
(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?
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
O There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.
O There is insufficient evidence at the 0.01 level to condude that the storm is increasing above the severe rating.
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Transcribed Image Text:(a) What is the level of significance? State the null and alternate hypotheses. O H: = 16.4 t; H,:< 16.4 ft O H: = 16.4 t; H: = 16.4 ft O H: H = 16.4 ft; H,: > 16.4 ft O Ho: A> 16.4 ft; H: = 16.4 ft OH: H< 16.4 ft; H,: = 16.4 ft (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and o is unknown. O The standard normal, since the sample size is large and o is known. O The Student's t, since the sample size is large and o is unknown. O The Student's t, since the sample size is large and o is known. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Estimate the P-value. O P-value > 0.250 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. o-3 -1 -2 -2 (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? O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. O There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating. O There is insufficient evidence at the 0.01 level to condude that the storm is increasing above the severe rating.
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