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 30 waves showed an average wave height of

*x* = 16.9 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?**

**(b) State the null and alternate
hypotheses.**

*H*_{0}: *?* = 16.4 ft;
*H*_{1}: *?* > 16.4 ft

*H*_{0}: *?* = 16.4 ft;
*H*_{1}: *?* < 16.4
ft

*H*_{0}: *?* = 16.4 ft;
*H*_{1}: *?* ? 16.4 ft

*H*_{0}: *?* > 16.4 ft;
*H*_{1}: *?* = 16.4 ft

*H*_{0}: *?* < 16.4 ft;
*H*_{1}: *?* = 16.4 ft

**(c) 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 known.

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

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

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

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

**(e) Estimate the P-value.**

*P*-value > 0.250

0.125 < *P*-value <
0.250

0.050 < *P*-value < 0.125

0.025 < *P*-value < 0.050

0.005 < *P*-value < 0.025

*P*-value < 0.005

**(f) Sketch the sampling distribution and show the area
corresponding to the P-value.**

**(g) 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.

**(h) 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.

Answer #1

a) Significance level,

b) Null and Alternative Hypothesis

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

**Answer:** The standard normal, since the sample
size is large and is known.

d)Under H0, the test statistic is

e) The P-Value is 0.217695

f)

g) Since p value is greater than significance level.

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

h) 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....

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....

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....

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