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 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

= 18.0 feet. Previous studies of severe storms indicate that σ = 4.0 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	=

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

Answer 1

Solution:

Given ,

= 16.4

claim : > 16.4

n = 31

= 18.0

= 4.0

Use = 0.01

a) Hypothesis are

H0 : = 16.4 (null hypo.)

H1 :   > 16.4 ..(alternative hypothesis)

b)The test statistic z is given by

z =

= (18.0 - 16.4) / (4.0/31)

= 2.23

Test statistic z = 2.23

c)Now , observe that ,there is > sign in H1. So , the test is right tailed.

So the critical value is i.e. _0.01

i.e. 2.33 (Use z table to find this value)

Critical region is z >   i.e. z >  2.33

Critical value = 2.33

d) z = 2.23 is less than = 2.33

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

e)For right tailed test :

p value = P(Z > 2.23)

= P(Z < -2.23)

= 0.0129 (use z table)

Since p value is greater than = 0.01 , we fail to reject the null hypothesis and there is insufficient evidence that the average storm level is increasing.

State your conclusion in the context of the application.

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?

The conclusions obtained by using both methods are the same.