Chapter 24, Problem 18E

(a)

To determine

Section 1:

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

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:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage of delayed }\\ \text{Alaska Airlines flights}\end{array}\right)=\frac{501}{3775}\times 100\\ =13.3\%\end{array}$

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:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage of delayed America}\\ \text{West Airlines flights}\end{array}\right)=\frac{787}{7225}\times 100\\ =10.9\%\end{array}$

(b)

Section 1:

To determine

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

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:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage of delayed Alaska}\\ \text{Airlines flights at Los Angeles}\end{array}\right)=\frac{62}{559}\times 100\\ =11.1\%\end{array}$

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:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage of delayed Alaska}\\ \text{ Airlines flights at Phoenix}\end{array}\right)=\frac{12}{233}\times 100\\ =5.2\%\end{array}$

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:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage of delayed Alaska}\\ \text{ Airlines flights at San Diego}\end{array}\right)=\frac{20}{232}\times 100\\ =8.6\%\end{array}$

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:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage of delayed Alaska}\\ \text{Airlines flights at San Francisco}\end{array}\right)=\frac{102}{605}\times 100\\ =16.9\%\end{array}$

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:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage of delayed Alaska}\\ \text{ Airlines flights at Seattle}\end{array}\right)=\frac{305}{2146}\times 100\\ =14.2\%\end{array}$

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:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage of delayed America West}\\ \text{ Airlines flights at Los Angeles}\end{array}\right)=\frac{117}{811}\times 100\\ =14.4\%\end{array}$

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:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage of delayed America}\\ \text{WestAirlines flights at Phoenix}\end{array}\right)=\frac{415}{5255}\times 100\\ =7.9\%\end{array}$

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:

$\begin{array}{c}\left(\begin{array}{l}\text{ Percentage of delayed America}\\ \text{West Airlines flights at San Diego}\end{array}\right)=\frac{65}{448}\times 100\\ =14.5\%\end{array}$

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:

$\begin{array}{c}\left(\begin{array}{l}\text{ Percentage of delayed America}\\ \text{ West Airlines flights at San Francisco}\end{array}\right)=\frac{129}{449}\times 100\\ =28.7\%\end{array}$

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:

$\begin{array}{c}\left(\begin{array}{l}\text{Percentage of delayed America}\\ \text{ West Airlines flights at Seattle}\end{array}\right)=\frac{61}{262}\times 100\\ =23.3\%\end{array}$

(c)

To determine

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

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.