Question

A random sample of n₁ = 14 winter days in Denver gave a sample mean pollution index x₁ = 43. Previous studies show that σ₁ = 21. For Englewood (a suburb of Denver), a random sample of n₂ = 12 winter days gave a sample mean pollution index of x₂ = 37. Previous studies show that σ₂ = 17. Assume the pollution index is normally distributed in both Englewood and Denver.

(a) Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance.

(i) What is the level of significance?

State the null and alternate hypotheses.

H₀: μ₁ = μ₂; H₁: μ₁ < μ₂

H₀: μ₁ = μ₂; H₁: μ₁ > μ₂     

H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂

H₀: μ₁ < μ₂; H₁: μ₁ = μ₂

(ii) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.     

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ₁ − μ₂. Round your answer to two decimal places.)

(iii) Find (or estimate) the P-value. (Round your answer to four decimal places.)

(iiii) Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

Answer 1

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