Statistics: Concepts and Controv. (Instructor's)
Statistics: Concepts and Controv. (Instructor's)
9th Edition
ISBN: 9781464193149
Author: Moore
Publisher: MAC HIGHER
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 24, Problem 18E

(a)

To determine

Section 1:

To find: The delayed percentage of all Alaska Airlines flights.

(a)

Expert Solution
Check Mark

Answer to Problem 18E

Solution: The percentage of delayed Alaska Airlines flights is 13.3%.

Explanation of Solution

Calculation:

Form the 2-way table for the number of delayed flights and on time flights for Alaska Airlines to determine the percentage for all the delayed Alaska Airlines flights. The 2-way table for Alaska Airlines is obtained as:

Airport Alaska Airlines
On time Delayed Total
Los Angeles 497 62 559
Phoenix 221 12 233
San Diego 212 20 232
San Francisco 503 102 605
Seattle 1841 305 2146
Total 3274 501 3775

There are 501 delayed flights out of total number of 3775 Alaska Airlines flights. So, the percentage of all Alaska Airlines delayed flights is calculated as:

(Percentage of delayed Alaska Airlines flights)=5013775×100=13.3%

Section 2:

To find: The delayed percentage of all America West Airlines flights.

Solution: The percentage of delayed America West Airlines flights is 10.9%.

Explanation:

Calculation:

Form the 2-way table for the number of delayed flights and on time flights for America West Airlines to determine the percentage for all the delayed America West Airlines flights. The two-way table for America West Airlines is obtained as:

Airport America West Airlines
On time Delayed Total
Los Angeles 694 117 811
Phoenix 4840 415 5255
San Diego 383 65 448
San Francisco 320 129 449
Seattle 201 61 262
Total 6438 787 7225

There are 787 delayed flights out of total number of 7225 America West Airlines flights. So, the percentage of all America West Airlines delayed flights is calculated as:

(Percentage of delayed AmericaWest Airlines flights)=7877225×100=10.9%

(b)

Section 1:

To determine

To find: The percentage of flights delayed at five airports for Alaska Airlines.

(b)

Section 1:

Expert Solution
Check Mark

Answer to Problem 18E

Solution: The percentage of flights delayed at five airports for Alaska Airlines is obtained as:

Airport Alaska Airlines Delayed percentage
Los Angeles 11.1%
Phoenix 5.2%
San Diego 8.6%
San Francisco 16.9%
Seattle 14.2%

Explanation of Solution

Calculation:

Use the two-way table obtained in previous part for delay of Alaska Airlines flight to determine the percentages of delayed flights at each one of the five airports.

From the obtained two-way table, the number of delayed flights of Alaska Airlines for Los Angeles airport is 62 flights from a total of 559 flights that arrive at the Los Angeles airport. So, the percentage of flights delayed at Los Angeles airport for Alaska Airlines is calculated as:

(Percentage of delayed AlaskaAirlines flights at Los Angeles)=62559×100=11.1%

The number of delayed flights of Alaska Airlines at Phoenix airport is 12 flights from a total of 233 flights that arrive at the Phoenix airport. So, the percentage of flights delayed at Phoenix airport for Alaska Airlines is calculated as:

(Percentage of delayed Alaska  Airlines flights at Phoenix)=12233×100=5.2%

The number of delayed flights of Alaska Airlines at San Diego airport is 20 flights from a total of 232 flights that arrive at the San Diego airport. So, the percentage of flights delayed at San Diego airport for Alaska Airlines is calculated as:

(Percentage of delayed Alaska Airlines flights at San Diego)=20232×100=8.6%

The number of delayed flights of Alaska Airlines at San Francisco airport is 102 flights from a total of 605 flights that arrive at the San Francisco airport. So, the percentage of flights delayed at San Francisco airport for Alaska Airlines is calculated as:

(Percentage of delayed AlaskaAirlines flights at San Francisco)=102605×100=16.9%

The number of delayed flights of Alaska Airlines at Seattle airport is 305 flights from a total of 2146 flights that arrive at the Seattle airport. So, the percentage of flights delayed at Seattle airport for Alaska Airlines is calculated as:

(Percentage of delayed Alaska   Airlines flights at Seattle)=3052146×100=14.2%

Section 2:

To find: The percentage of flights delayed at five airports for America West Airlines.

Solution: The percentage of flights delayed at five airports for America West Airlines is obtained as:

Airport America West Airlines Delayed percentage
Los Angeles 14.4%
Phoenix 7.9%
San Diego 14.5%
San Francisco 28.7%
Seattle 23.3%

Explanation:

Calculation:

Use the two-way table obtained in previous part for delay of America West Airlines flight to determine the percentages of delayed flights at each one of the five airports.

From the obtained two-way table, the number of delayed flights of America West Airlines for Los Angeles airport is 117 flights from a total of 811 flights that arrive at the Los Angeles airport. So, the percentage of flights delayed at Los Angeles airport for America West Airlines is calculated as:

(Percentage of delayed America West Airlines flights at Los Angeles)=117811×100=14.4%

The number of delayed flights of America West Airlines at Phoenix airport is 415 flights from a total of 5255 flights that arrive at the Phoenix airport. So, the percentage of flights delayed at Phoenix airport for America West Airlines is calculated as:

(Percentage of delayed AmericaWestAirlines flights at Phoenix)=4155255×100=7.9%

The number of delayed flights of America West Airlines at San Diego airport is 65 flights from a total of 448 flights that arrive at the San Diego airport. So, the percentage of flights delayed at San Diego airport for America West Airlines is calculated as:

(  Percentage of delayed AmericaWest Airlines flights at San Diego)=65448×100=14.5%

The number of delayed flights of America West Airlines at San Francisco airport is 129 flights from a total of 449 flights that arrive at the San Francisco airport. So, the percentage of flights delayed at San Francisco airport for America West Airlines is calculated as:

(     Percentage of delayed America West Airlines flights at San Francisco)=129449×100=28.7%

The number of delayed flights of America West Airlines at Seattle airport is 61 flights from a total of 262 flights that arrive at the Seattle airport. So, the percentage of flights delayed at Seattle airport for America West Airlines is calculated as:

(Percentage of delayed America West Airlines flights at Seattle)=61262×100=23.3%

(c)

To determine

The reason for America West to have a better performance overall but worse at each one of the five airports.

(c)

Expert Solution
Check Mark

Answer to Problem 18E

Solution: The overall performance of America West Airline is better even though it is worse at each one of the five airports as the weather at the airport that flights serve is a lurking variable which reverses the relationship as per Simpson’s paradox.

Explanation of Solution

Calculation:

The provided data shows that the America West performance is worst at every one of the airport but its overall performance is better because of the weather in Phoenix and Seattle gives an overall better performance.

According to Simpson’s paradox, the effect of lurking variables changes or reverses the relationships between categorical variables. In the provided problem, the weather in Phoenix and Seattle is a lurking variable that reverses the relationship and hence the overall performance is better even though it is worse at each one of the five airports.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY