In the airline business, "on-time" flight arrival is important for connecting flights and general customer satisfaction. Is there a difference between summer and winter average on-time flight arrivals? Let x, be a random variable that represents percentage of on-time arrivals at major airports in the summer. Let x, be a random variable that represents percentage of on- time arrivals at major airports in the winter. A random sample of n₁ = 16 major airports showed that x₁ = 74.9%, with s₁ = 5.2%. A random sample of n₂ = major airports showed that x2 = 70.1%, with s₂ = 8.7%. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. (a) Does this information indicate a difference (either way) in the population mean percentage of on-time arrivals for summer compared to winter? Use α = 0.05. (i) What is the level of significance? 0.05 State the null and alternate hypotheses. OH H₁ = Hy Hy! Hy 0.500 O 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 P-value <0.100 0.010 P-value < 0.050 OP-value <0.010 Sketch the sampling distribution and show the area corresponding to the P-value. ° -3 -2 -1 0 1 3 -2 -1 0 1 2 3 -3 -1 0 1 2 3 O -3 -2 0 2 (iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (b) Find a 95% confidence interval for μ-μ₂. (Round your answers to two decimal places.) lower limit upper limit % % (c) What assumptions about the original populations have you made for the methods used? ○ We assume that x₁ and x, are skewed right. ○ We assume that x and x, are approximately normal or at least mound-shaped and symmetric. 1 We assume that x, and x, are skewed left.

In the airline business, "on-time" flight arrival is important for connecting flights and general customer satisfaction. Is there a difference between summer and winter average on-time flight arrivals? Let x, be a random variable that represents percentage of on-time arrivals at major airports in the summer. Let x, be a random variable that represents percentage of on- time arrivals at major airports in the winter. A random sample of n₁ = 16 major airports showed that x₁ = 74.9%, with s₁ = 5.2%. A random sample of n₂ = major airports showed that x2 = 70.1%, with s₂ = 8.7%. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. (a) Does this information indicate a difference (either way) in the population mean percentage of on-time arrivals for summer compared to winter? Use α = 0.05. (i) What is the level of significance? 0.05 State the null and alternate hypotheses. OH H₁ = Hy Hy! Hy 0.500 O 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 P-value <0.100 0.010 P-value < 0.050 OP-value <0.010 Sketch the sampling distribution and show the area corresponding to the P-value. ° -3 -2 -1 0 1 3 -2 -1 0 1 2 3 -3 -1 0 1 2 3 O -3 -2 0 2 (iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (b) Find a 95% confidence interval for μ-μ₂. (Round your answers to two decimal places.) lower limit upper limit % % (c) What assumptions about the original populations have you made for the methods used? ○ We assume that x₁ and x, are skewed right. ○ We assume that x and x, are approximately normal or at least mound-shaped and symmetric. 1 We assume that x, and x, are skewed left.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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