Homework Help is Here – Start Your Trial Now!
Math
Statistics
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.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
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 <Hz H₁₁ =H₂ H₁: My #Hz OH₁₁ = H₁: Hy » Hz OHHHHH₂ = H₂ (ii) 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. O 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. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? (Round your answer to three decimal places.) (iii) Find (or estimate) the P-value. O P-value > 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.
Transcribed Image Text: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 <Hz H₁₁ =H₂ H₁: My #Hz OH₁₁ = H₁: Hy » Hz OHHHHH₂ = H₂ (ii) 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. O 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. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? (Round your answer to three decimal places.) (iii) Find (or estimate) the P-value. O P-value > 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.
Transcribed Image Text:(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.
Expert Solution
steps

Step by step

Solved in 2 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS