Question

how do i find a critical value in a hypothesis testing? with steps please!

For example,

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 μ = 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 31 waves showed an average wave height of x = 17.2 feet. Previous studies of severe storms indicate that σ = 3.1 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to two decimal places.)

Answer 1

H0: mu = 16.4
Ha: mu > 16.4

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (17.2 - 16.4)/(3.1/sqrt(31))
z = 1.44

This is right tailed test, hence the critical value will be on the right of the normal curve
in order to find the critical value, find the value of z such that P(z > a) = 0.01

Using right tailed z-table, we get critical value = 2.33
Reject H0, if test statistic > 2.33

Fail to reject H0
There are not sufficient evidence to suggest that the storm is (perhaps temporarily) increasing above the severe rating