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 = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01.

(a) What is the level of significance?

(b) What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.4 with sample standard deviation s = 2.7. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

(a) What is the level of significance?

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)