Question

A fair coin is flipped 90 times. The probability that more than two-thirds of the tosses result in tails is 0.0008. Is this convincing evidence against the claim that the coin is fair?

a. Yes, the probability of seeing the sample result is so far from what we expected that the probability of it occurring by chance alone is very unlikely
b. Yes, we would expect half of the tosses to result in heads. The difference between half and two-thirds is too large to have happened by accident.
c. No, the difference between the sample result and what we expected is not extreme enough.
d. No, there is an extremely small chance of seeing the sample result. It must have occurred by chance alone.

Answer 1

The very low probability of obtaining more than two-thirds tails in 90 tosses of a fair coin is convincing evidence against the coin being fair and indicates this skewed result is unlikely due to chance alone.

Step-by-step explanation:

The probability of seeing more than two-thirds of the tosses result in tails when a fair coin is flipped 90 times is 0.0008. Given that a fair coin should land on heads or tails with an equal chance of 50%, such a low probability (0.0008) for a highly skewed result provides convincing evidence against the coin being fair. This extreme deviation from the expected ratio of heads to tails is not what we would expect if the coin were indeed fair.

Answer option a is the correct choice because the probability is significantly lower than the standard 5 percent significance level typically used in hypothesis testing to determine if an event occurs by chance. Therefore, seeing such a skewed result (more than two-thirds tails) suggests that something other than chance may be influencing the outcomes, which may indicate that the coin is not fair.