A random sample of n1 = 16 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that ?1 = 15. For Englewood (a suburb of Denver), a random sample of n2 = 14 winter days gave a sample mean pollution index of x2 = 37. Previous studies show that ?2 = 17. 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: ?1 < ?2; H1: ?1 = ?2H0: ?1 = ?2; H1: ?1 > ?2 H0: ?1 = ?2; H1: ?1 ≠ ?2H0: ?1 = ?2; H1: ?1 < ?2 (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 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.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? (Test the difference ?1 − ?2. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

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Description: A random sample of n1 = 16 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that ?1 = 15. For Englewood (a suburb of Denver), a random sample of n2 = 14 winter days gave a sample mean pollution index of x2 = 37.

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

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ISBN:9780079039897

Author:Carter

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Chapter10: Statistics

Section10.1: Measures Of Center

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A random sample of n₁ = 16 winter days in Denver gave a sample mean pollution index x₁ = 43. Previous studies show that ?₁ = 15. For Englewood (a suburb of Denver), a random sample of n₂ = 14 winter days gave a sample mean pollution index of x₂ = 37. Previous studies show that ?₂ = 17. 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: ?₁ < ?₂; H₁: ?₁ = ?₂H₀: ?₁ = ?₂; H₁: ?₁ > ?₂ H₀: ?₁ = ?₂; H₁: ?₁ ≠ ?₂H₀: ?₁ = ?₂; H₁: ?₁ < ?₂

(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 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.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? (Test the difference ?₁ − ?₂. 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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