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 38 waves showed an average wave height of x = 16.9 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. State the null and alternate hypotheses. H0: ? > 16.4 ft; H1: ? = 16.4 ft H0: ? = 16.4 ft; H1: ? < 16.4 ft H0: ? = 16.4 ft; H1: ? > 16.4 ft H0: ? < 16.4 ft; H1: ? = 16.4 ft H0: ? = 16.4 ft; H1: ? ≠ 16.4 ft What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and ? is unknown. The standard normal, since the sample size is large and ? is known. The Student's t, since the sample size is large and ? is unknown. The Student's t, since the sample size is large and ? is known. What is the value of the sample test statistic? (Round your answer to two decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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 38 waves showed an average wave height of x = 16.9 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.
State the null and alternate hypotheses.
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