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Weatherwise is a magazine published by the AmericanMeteorological Society. One issue gives a rating system used toclassify Nor'easter storms that frequently hit New England and cancause much damage near the ocean. A severe storm has an averagepeak wave height of μ = 16.4 feet for waves hitting theshore. Suppose that a Nor'easter is in progress at the severe stormclass rating. Peak wave heights are usually measured from land(using binoculars) off fixed cement piers. Suppose that a readingof 35 waves showed an average wave height of x = 17.7feet. Previous studies of severe storms indicate that σ =3.5 feet. Does this information suggest that the storm is (perhapstemporarily) 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 ftH₀:μ = 16.4 ft; H₁: μ > 16.4ft    H₀: μ = 16.4ft; H₁: μ < 16.4ftH₀: μ < 16.4 ft;H₁: μ = 16.4 ftH₀:μ = 16.4 ft; H₁: μ ≠ 16.4ft

(b) What sampling distribution will you use? Explain the rationalefor your choice of sampling distribution.

The Student's t, since the sample size is large andσ is known.The standard normal, since the sample size islarge and σ is known.    The standardnormal, since the sample size is large and σ isunknown.The Student's t, since the sample size is largeand σ is unknown.

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


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


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

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis? Are the data statisticallysignificant at level α?

At the α = 0.01 level, we reject the null hypothesisand conclude the data are statistically significant.At theα = 0.01 level, we reject the null hypothesis and concludethe data are not statisticallysignificant.    At the α = 0.01 level,we fail to reject the null hypothesis and conclude the data arestatistically significant.At the α = 0.01 level, we failto reject the null hypothesis and conclude the data are notstatistically significant.