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 30 waves showed an average wave height of

x

= 17.1 feet. Previous studies of severe storms indicate that σ = 3.7 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.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.

Answer 1

Given that, population standard deviation = 3.7 feet

sample size (n) = 30 and sample mean = 17.1 feet

The null and alternative hypotheses are,

H0 : μ = 16.4 feet

Ha : μ > 16.4 feet

Test statistic is,

=> Test statistic = 1.04

Critical value Method :

critical value at significance level of 0.01 is, Z_{​​​​​​crit} = 2.33

=> Critical value = 2.33

Since, z = 1.04 < 233, we fail to reject H0.

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

P-value Method :

p-value = P(Z > 1.04) = 1 - P(Z < 1.04) = 1 - 0.8508 = 0.1492

=> p-value = 0.1492

Since, p-value > 0.01, we fail to reject H0.

Therefore, the conclusions obtained by using both methods are the same.