A random sample of n1 = 20 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that σ1 = 11. For Englewood (a suburb of Denver), a random sample of n2 = 10 winter days gave a sample mean pollution index of x2 = 31. Previous studies show that σ2 = 18. Assume the pollution index is normally distributed in both Englewood and Denver. 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. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ1 < μ2; H1: μ1 = μ2H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2H0: μ1 = μ2; H1: μ1 < μ2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student's t. We assume that both population distributions are approximately normal with known 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 unknown standard deviations. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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ISBN:9780079039897

Author:Carter

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A random sample of n₁ = 20 winter days in Denver gave a sample mean pollution index x₁ = 43. Previous studies show that σ₁ = 11. For Englewood (a suburb of Denver), a random sample of n₂ = 10 winter days gave a sample mean pollution index of x₂ = 31. Previous studies show that σ₂ = 18. Assume the pollution index is normally distributed in both Englewood and Denver. 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.

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀: μ₁ < μ₂; H₁: μ₁ = μ₂H₀: μ₁ = μ₂; H₁: μ₁ > μ₂ H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂H₀: μ₁ = μ₂; H₁: μ₁ < μ₂

(b)

What sampling distribution will you use? What assumptions are you making?

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

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to two decimal places.)

(c)

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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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