Question

a magician flips a coin 8 times producing heads each time. is there statistical significance to say that the coin is somehow rigged? a. yes, because the results are likely to happen by chance. b. no, because the results are unlikely to happen by chance. c. no, because the results are likely to happen by chance. d. yes, because the results are unlikely to happen by chance.

Explanation:

A fair coin has a 0.5 chance of heads per flip. The probability of 8 consecutive heads is \(0.5^8 = \frac{1}{256}\), which is very low (unlikely by chance). Statistical significance for rigging is when results are unlikely by chance, so we conclude the coin is likely rigged (yes, due to low chance of random occurrence).

Answer:

D. Yes, because the results are unlikely to happen by chance.