A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a storm is in progress with a severe storm class rating. Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis? Is the P-value area on the left, right, or on both sides of the mean?
a. H1: \mu is greater than 16.4 feet; the P-value area is on the left of the mean
b. H1: \mu is less than 16.4 feet; the P-value area is on the left of the mean
c. H1: \mu is greater than 16.4 feet; the P-value area is on both sides of the mean
d. H1: \mu is not equal to 16.4 feet; the P-value area is on the left of the mean
To set up a statistical test, we first need to determine the null hypothesis (H0) and the alternative hypothesis (H1). In this case, we want to test if the wave action is dying down, so the null hypothesis would be that the average peak wave height remains the same or increases.
For the alternate hypothesis (H1), we want to test if the waves are dying down, which means that the average peak wave height is less than 16.4 feet. Therefore, the correct option would be:
b. H1: μ is less than 16.4 feet; the P-value area is on the left of the mean
The P-value area represents the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true. Since we are testing if the average peak wave height is less than 16.4 feet (a one-tailed test), the P-value area is on the left side of the mean.