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Suppose at a local casino, a player rolls $4$ six-sided die.

The player wins a dollar each time he gets a $1$ or $2$ on one of the dice, so each game the player could win anywhere from $\$0$ to $\$4$.

The player plays the game $100$ times and is disappointed with the outcome. He wonders if the dice are fair. Out of the $100$ trials, the player ended up with the following distribution of winnings:

Winnings \$0 \$1 \$2 \$3 \$4
Frequency 21 42 30 7 0

Is there sufficient evidence the dice are unfair?


Yes, at the $1\%, 5\%$, and $10\%$ alpha levels.


Yes, at the $5\%$ and $10\%$ alpha levels, but not at the $1\%$ level.


Yes, at the $10\%$ alpha level, but not the $1\%$ or $5\%$ levels.


No, not at any of the common alpha levels of $1\%, 5\%$, or $10\%$.


No, in fact, there is strong evidence the game is fair.

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