Question

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 36 waves showed an average wave height of x = 17.3 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?


State the null and alternate hypotheses.

H₀: μ < 16.4 ft; H₁: μ = 16.4 ft H₀: μ = 16.4 ft; H₁: μ > 16.4 ft     H₀: μ = 16.4 ft; H₁: μ < 16.4 ft H₀: μ > 16.4 ft; H₁: μ = 16.4 ft H₀: μ = 16.4 ft; H₁: μ ≠ 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 σ is known. The Student's t, since the sample size is large and σ is unknown.     The standard normal, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ is unknown.

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.)


Sketch the sampling distribution and show the area corresponding to the P-value.

Answer 1