Question

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 35 waves showed an average wave height of x = 17.7 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 ftH₀: μ = 16.4 ft; H₁: μ > 16.4 ft    H₀: μ = 16.4 ft; H₁: μ < 16.4 ftH₀: μ < 16.4 ft; H₁: μ = 16.4 ftH₀: 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 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.The Student's t, 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.

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

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

Answer 1

1. (a) What is the level of significance?

alpah=0.01

State the null and alternate hypotheses.

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.

since sigma known its z distribution

The standard normal, since the sample size is large and σ is known

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

z=xbar-mu/sigma/sqrt(n)

=(17.7-16.4)/(3.5/sqrt(35))

=2.197401

Z=2.20

value of the sample test statistic=z=2.20

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

p=0.01399=0.0140

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

p>0.01

Fail to reject Ho

  At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

H0: μ = 16.4 ft;

H1: μ > 16.4 ft

The standard normal, since the sample size is large and σ is known
Z=2.20

  At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.