All answers have to be guesses, but let’s test our statistical intuition.
With 4:30 left in the Cotton Bowl game, Southern Cal kicks a field goal to make the score 45 – 30. With what confidence (68%, 95%, etc) would you say that USC will win the game?
With 4:07 left in the game, Tulane scores a touchdown and kicks the PAT to make the score 45 – 37. How does that change your confidence that USC will win the game?
USC mishandles the ensuing kick-off and starts inside its own 5 yard line. Confidence level?
On the second play, USC is tackled for a safety, making the score 45 -39 with 3:20 left. Confidence level?
9 seconds left, Tulane scores a touchdown, tying the score at 45. Confidence level?
Tulane kicks the PAT, taking the lead at 46 – 45. Confidence level?
USC attempts to lateral its way down the field but fails.
Lesson: There are events in the tails of statistical distributions, and they can and do occur. A 95% confidence level is not a guarantee of correctness.
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