Question

Weatherwise magazine is published in association with the American Meteorological Society. Volume 46, Number 6 has a rating system to classify Nor'easter storms that frequently hit New England states and can cause much damage near the ocean coast. 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.

(a) Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. What would be the null hypothesis regarding average wave height?

μ < 16.4μ ≠ 16.4    μ > 16.4μ = 16.4

(b) If you wanted to test the hypothesis that the storm is getting worse, what would you use for the alternate hypothesis?

μ > 16.4μ = 16.4    μ < 16.4μ ≠ 16.4

(c) If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis?

μ = 16.4μ ≠ 16.4    μ < 16.4μ > 16.4

(d) Suppose you do not know if the storm is getting worse or dying out. You just want to test the hypothesis that the average wave height is different (either higher or lower) from the severe storm class rating. What would you use for the alternate hypothesis?

μ > 16.4μ < 16.4    μ ≠ 16.4μ = 16.4

(e) For each of the tests in parts (b), (c), and (d), would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean?

left; right; bothright; left; both    both; left; rightleft; both; right

Answer 1

Two ground rules before we answer this-

Null Hypothesis:

• Denoted by H0
• Always contains the equality sign

Alternate Hypothesis:

• Denoted by Ha
• Never contains the equality (Has <, > or Not equals to)

Now let us answer this question,

For a severe storm, we have the average peak wave height, μ = 16.4 ft

(a) In this, we want to know if the wave action (i.e., height) is dying down

We need to find out that the height is falling below the mean height or not

So, H0: μ = 16.4

(b)

We need to test the hypothesis that the storm is getting worse

It means that the height of the wave is increasing

Ha: μ > 16

(c)

We are testing the hypothesis that the waves are dying down

Ha: μ < 16

(d)

The average wave height is different

So, Ha: μ ≠ 16

(e)

b- right

c- left

d- both

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