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 μ = 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 35 waves showed an average wave height of x = 16.5 feet. Previous studies of severe storms indicate that σ = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01.

(a) What is the level of significance?

State the null and alternate hypotheses.

H0: μ = 16.4 ft; H1: μ ≠ 16.4 ft

H0: μ < 16.4 ft; H1: μ = 16.4 ft

H0: μ > 16.4 ft; H1: μ = 16.4 ft

H0: μ = 16.4 ft; H1: μ > 16.4 ft

H0: μ = 16.4 ft; H1: μ < 16.4 ft

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

The standard normal, since the sample size is large and σ is known.

The Student's t, since the sample size is large and σ is known.

The Student's t, since the sample size is large and σ is unknown.

The standard normal, since the sample size is large and σ is unknown.

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

(c) Estimate the

P-value. P-value > 0.250

0.100 < P-value < 0.250

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

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 α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant

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

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

At the α = 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. There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating. There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.

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 = 17.8 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.

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.

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 unknown.

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

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


(c) Find the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(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 ??

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

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

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

At the ? = 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.

There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.

There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.     

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 μ = 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 = 16.7 feet. Previous studies of severe storms indicate that σ = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 16.4 ft; H₁:  μ ≠ 16.4 ftH₀: μ > 16.4 ft; H₁:  μ = 16.4 ft     H₀: μ = 16.4 ft; H₁:  μ < 16.4 ftH₀: μ < 16.4 ft; H₁:  μ = 16.4 ftH₀: μ = 16.4 ft; H₁:  μ > 16.4 ft

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

The standard normal, since the sample size is large and σ is unknown.The Student's t, since the sample size is large and σ is known.     The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is unknown.

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


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250     0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(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 α?

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

There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.     

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 μ = 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 31 waves showed an average wave height of x = 17.3 feet. Previous studies of severe storms indicate that σ = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01.

(a) What is the level of significance?______


State the null and alternate hypotheses.

A) H₀: μ = 16.4 ft; H₁: μ ≠ 16.4 ft

B) H₀: μ > 16.4 ft; H₁: μ = 16.4 ft    

C) H₀: μ < 16.4 ft; H₁: μ = 16.4 ft

D) H₀: μ = 16.4 ft; H₁: μ < 16.4 ftH₀: μ = 16.4 ft; H₁: μ > 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 σ is unknown.

B) The standard normal, since the sample size is large and σ is unknown.    

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

D)The standard normal, since the sample size is large and σ is known.

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

(c) Estimate the P-value.

A) P-value > 0.2500.100 < P-value < 0.250    

B) 0.050 < P-value < 0.1000

C) .010 < P-value < 0.050

D) 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 α?

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

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

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

D) At the α = 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.

A) There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.

B)There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.

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 μ = 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 33 waves showed an average wave height of

x

= 17.3 feet. Previous studies of severe storms indicate that σ = 3.1 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to two decimal places.)

State your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the average storm level is increasing.

Reject the null hypothesis, there is insufficient evidence that the average storm level is increasing.    

Fail to reject the null hypothesis, there is sufficient evidence that the average storm level is increasing.

Fail to reject the null hypothesis, there is insufficient evidence that the average storm level is increasing.

Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?

We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.

We reject the null hypothesis using the traditional method, but fail to reject using the P-value method.    

The conclusions obtained by using both methods are the same.

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 μ = 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

= 17.0 feet. Previous studies of severe storms indicate that σ = 3.3 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to two decimal places.)

State your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the average storm level is increasing. Reject the null hypothesis, there is insufficient evidence that the average storm level is increasing.     Fail to reject the null hypothesis, there is sufficient evidence that the average storm level is increasing. Fail to reject the null hypothesis, there is insufficient evidence that the average storm level is increasing.

Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?

We reject the null hypothesis using the traditional method, but fail to reject using the P-value method. The conclusions obtained by using both methods are the same.     We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.

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 μ = 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 30 waves showed an average wave height of x = 17.3 feet. Previous studies of severe storms indicate that σ = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01.

What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 16.4 ft; H₁:  μ < 16.4 ftH₀: μ = 16.4 ft; H₁:  μ > 16.4 ft     H₀: μ > 16.4 ft; H₁:  μ = 16.4 ftH₀: μ = 16.4 ft; H₁:  μ ≠ 16.4 ftH₀: μ < 16.4 ft; H₁:  μ = 16.4 ft

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

The Student's t, since the sample size is large and σ is unknown.The Student's t, since the sample size is large and σ is known.     The standard normal, since the sample size is large and σ is unknown.The standard normal, since the sample size is large and σ is known.

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


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250     0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(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 α?

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

There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.     

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 μ = 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 x = 16.7 feet. Previous studies of severe storms indicate that σ = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01.

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

The standard normal, since the sample size is large and σ is known.The standard normal, since the sample size is large and σ is unknown.    The Student's t, since the sample size is large and σ is unknown.The Student's t, since the sample size is large and σ is known.

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

(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250    0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(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 α?

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

There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.  

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 μ = 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 34 waves showed an average wave height of x = 17.7 feet. Previous studies of severe storms indicate that σ = 3.8 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to two decimal places.) test statistic = critical value =

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 μ = 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 = 17.0 feet. Previous studies of severe storms indicate that σ = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 16.4 ft; H₁:  μ ≠ 16.4 ftH₀: μ = 16.4 ft; H₁:  μ > 16.4 ft     H₀: μ > 16.4 ft; H₁:  μ = 16.4 ftH₀: μ < 16.4 ft; H₁:  μ = 16.4 ftH₀: μ = 16.4 ft; H₁:  μ < 16.4 ft

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

The Student's t, since the sample size is large and σ is known.The standard normal, since the sample size is large and σ is unknown.     The Student's t, since the sample size is large and σ is unknown.The standard normal, since the sample size is large and σ is known.

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


(c) Find the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(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 α?

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

There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.