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 31 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 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.

The Student's t, 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.) ________________

(c) Estimate the P-value.

P-value > 0.250

0.100 < P-value < 0.250

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

2.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 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 3.0. 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?


State the null and alternate hypotheses.

H₀: μ = 7.4; H₁:  μ ≠ 7.4H₀: μ ≠ 7.4; H₁:  μ = 7.4     H₀: μ > 7.4; H₁:  μ = 7.4H₀: μ = 7.4; H₁:  μ > 7.4H₀: μ = 7.4; H₁:  μ < 7.4

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

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.     

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

The Student's t, since the sample size is large and σ is known.

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

Answer 1

1. a) Let the los be alpha= 0.01

Correct answer: Option H1: μ = 16.4 ft H0: μ > 16.4 ft;

From the given data

b) Correct answer: The standard normal, since the sample size is large and σ is known.

c)

P-Value: 0.0761

Correct answer: 0.050 < P-value < 0.100

Here P-value > alpha 0.01, so we accept H0

Thus we conclude that μ = 16.4 ft

2.

a) Let the los be alpha = 5%

Correct answer: H₀: μ = 7.4; H₁:  μ ≠ 7.4

b) Correct answer: The Student's t, since the sample size is large and σ is unknown.

c)

P-Value: 0.0336

Here P-value < alpha 0.05 so we do not accept H0

Thus we conclude that μ ≠ 7.4