Question

2.7. Here are the numbers of flights on time and delayed for two airlines at five airports in one month. Overall on-time percent's for each airline are often reported in the news. The airport that flights serve is a lurking variable that can make such reports misleading Alaska Airlines America West On time 497 221 212 503 1841 On time 694 4840 383 320 201 Delayed Los Angeles San Diego San Francisco Seattle 62 12 20 102 305 415 65 129 61 What percent of all Alaska Airlines flights were delayed? What percent of all America West flights were delayed? These are the numbers usually Now find the percent of delayed flights for Alaska Airlines at each of the five airports. Do the same for America West. America West did worse at every one of the five airports, yet did better overall. That sounds impossible. Explain carefully, referring to the data, how this can happen.

Answer 1

Percent of Alaska Airline flights that were delayed = (62+12+20+102+305)/(497+221+212+503+1841+62+12+20+102+305) x 100

= 501/3775 x 100

= 13.27%

Percent of America West flights that were delayed = (117+415+65+129+61)/(694+4840+383+320+201+117+415+65+129+61) x 100

= 787/7225 x 100

= 10.89%

	% of Alaska Airline delayed	% of America West delayed
Los Angeles	11.09	14.43
Phoenix	5.15	8.57
San Diego	8.62	14.51
San Francisco	16.86	28.73
Seattle	14.21	23.28

The impossible looking observation is because of the high count of America West flights in Phoenix airport. The percentage of America West delayed in Phoenix is less than the total percentage of delayed flights of Alaska Airlines. So, when we compute the total number of delayed flights and thereby calculating the percentage of delayed flights, higher weightage goes to the delayed America West category. As a result, the overall percentage of America west delayed flights are close to the percentage of delayed flights from Phoenix.