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 u = 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 40 waves showed an average wave height of x = 17.3 feet. Previous studies of severe storms indicate that o = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. O Họ: H > 16.4 ft; H: H= 16.4 ft O Họ: H = 16.4 ft; Hz: µ < 16.4 ft O Ho: H = 16.4 ft; H;: µ * 16.4 ft O Ho: H< 16.4 ft; H: H- 16.4 ft O Họ: H= 16.4 ft; H: H> 16.4 ft (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and o is unknown. O The standard normal, since the sample size is large and a is unknown. O The standard normal, since the sample size is large and a is known. 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
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 u = 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 40 waves showed an average wave height of x = 17.3 feet. Previous studies of severe storms indicate that o = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. O Họ: H > 16.4 ft; H: H= 16.4 ft O Họ: H = 16.4 ft; Hz: µ < 16.4 ft O Ho: H = 16.4 ft; H;: µ * 16.4 ft O Ho: H< 16.4 ft; H: H- 16.4 ft O Họ: H= 16.4 ft; H: H> 16.4 ft (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and o is unknown. O The standard normal, since the sample size is large and a is unknown. O The standard normal, since the sample size is large and a is known. 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
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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 u = 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 40 waves showed an average wave height of x = 17.3 feet. Previous studies of severe storms indicate that o = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use a = 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses.
O Ho: µ > 16.4 ft; H1: µ = 16.4 ft
Но: и %3D 16.4 ft; Hi: и < 16.4 ft
O Ho: H = 16.4 ft; H1: µ ± 16.4 ft
О Но: и < 16.4 ft; Hi: и %3 16.4 ft
Но: и %3D 16.4 ft;B Hi: и > 16.4 ft
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The Student's t, since the sample size is large and o is unknown.
The standard normal, since the sample size is large and o is unknown.
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 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
0.010 < P-value < 0.050
O P-value < 0.010
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value.
-2
-1
1
2
3
-2
-1
1
3
3
-2
-1
1
3
0-3
-2
-1
1
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 conclude that the storm is increasing above the severe rating.
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