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 34 waves showed an average wave height of x = 17.3 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?1What is the value of the sample test statistic? (Round your answer to two decimal places.)

Answer 1

Answer:

We conclude that the storm is not increasing above the severe rating.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 16.4 feet

Sample mean, $\bar{x}$ = 17.3 feet

Sample size, n = 34

Alpha, α = 0.01

Population standard deviation, σ = 3.5 feet

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 16.4\text{ feet}\\H_A: \mu > 16.4\text{ feet}$

We use One-tailed(right) z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{17.3 - 16.4}{\frac{3.5}{\sqrt{34}} } = 1.49$

Now, $z_{critical} \text{ at 0.01 level of significance } = 2.33$

Since,  

$z_{stat} < z_{critical}$

We fail to reject the null hypothesis and accept null hypothesis. Thus, the  the storm is not increasing above the severe rating.