a) What is the level of significance? State the null and alternate hypotheses. H0: ? = 16.4 ft; H1: ? > 16.4 ftH0: ? = 16.4 ft; H1: ? ≠ 16.4 ft H0: ? > 16.4 ft; H1: ? = 16.4 ftH0: ? = 16.4 ft; H1: ? < 16.4 ftH0: ? < 16.4 ft; H1: ? = 16.4 ft (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and ? is unknown.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 known. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Estimate the P-value. P-value > 0.2500.100 < P-value < 0.250 0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010
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 32 waves showed an average wave height of x = 16.7 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.
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Estimate the P-value.
Sketch the sampling distribution and show the area corresponding to the P-value.
xbar = 16.7
mu = 16.4
s =3.5
n=32
Step by step
Solved in 2 steps with 3 images
