Below we give two contingency tables of data from reports submitted by airlines to the U.S. Department of Transportation. The data concern the numbers of on-time and delayed flights for Alaska Airlines and America West Airlines at five major airports.

a. What percentage of all Alaska Airlines flights were delayed? That is, use the data to estimate the probability that an Alaska Airlines flight will be delayed. Do the same for America West Airlines. Which airline does best overall?
b. For Alaska Airlines, find the percentage of delayed flights at each airport. That is, use the data to estimate each of the probabilities P(delayed | Los Angeles), P(delayed | Phoenix), and so on. Then do the same for America West Airlines. Which airline does best at each individual airport?
c. We find that America West Airlines does worse at every airport, yet America West does best overall. This seems impossible, but it is true! By looking carefully at the data, explain how this can happen. Hint: Consider the weather in Phoenix and Seattle. (This exercise is an example of what is called Simpson's paradox.)

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Alaska Airlines America West On Time Delayed Total 559 233 232 605 2,146 3,775 Delayed Los Angeles Phoenix San Diego San Francisco Seattle Total 497 221 212 503 1,841 3,274 62 12 20 102 305 501 Los Angeles Phoenix San Diego San Francisco Seattle Total On Time 694 4,840 383 320 201 6,438 415 65 129 61 787 Total 811 5,255 448 449 262 7,225