Earlier Problem Revisited

Suppose you were at a county fair and saw a large jar full of gumballs, maybe 1000 of them, with a sign that said “Guess the Number, Win a Prize!” If the rules of the game are that you could win a $10 prize by guessing within 200 gumballs either way, or a $50 prize by guessing within five gumballs either way, but you have to specify which prize you are trying for before submitting your guess, which would you choose?

This problem/question is meant to give you an intuitive feeling for the concept of a confidence interval or confidence level. It should be clear that you would have a greater level of confidencein trying for a $10 prize that you would win simply by guessing within +/- 20% of the number, than in trying for $50 by guessing within +/- 0.5% of the number!