Question

Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms. 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. Does the information suggest that the storm is perhaps temporarily increasing above the severe rating? Use a level of significance of 0.01.

What is the level of significance?
State the null and alternate hypotheses.
What sampling distribution will you use? Explain the rationale for your choice.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
Estimate the p-value.

Answer 1

The question involves hypothesis testing to determine if a Nor'easter storm increases above the severe rating based on peak wave heights, with a level of significance at 0.01. Without actual data, the sample test statistic and p-value cannot be calculated or estimated.

Step-by-step explanation:

The question involves using hypothesis testing to determine if a Nor'easter storm increases above the severe rating, with a focus on peak wave heights. The level of significance is given as 0.01, which is the probability threshold below which we will reject the null hypothesis. The null hypothesis (H0) would be that the storm has not increased above the severe rating, which means that the average peak wave height does not exceed 16.4 feet. The alternative hypothesis (H1) is that the storm has temporarily increased above the severe rating, which would mean the average peak wave height is greater than 16.4 feet.

Since the actual peak wave heights are not provided, we cannot calculate the sample test statistic or estimate the p-value. However, the sampling distribution would typically be the t-distribution if we had sufficient sample size and the sample standard deviation was known, assuming peak wave heights follow a normal distribution. If we had the value of the sample test statistic, it would be rounded to two decimal places as per the student's instructions.

If the calculated p-value were less than the level of significance (0.01), we would reject the null hypothesis, indicating that it's likely the storm has indeed increased above the severe rating. Unfortunately, without the actual data, the test statistic and p-value cannot be provided.