AnswersNC-Math 4Calculating Probabilities for Sampling DistributionQuestion 164005
164005
AssignmentMultiple Choice

Calculating Probabilities for Sampling Distribution

Question 164005 • NC-Math 4

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?

Answer
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 (0.0008 < 0.05).
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.

Explanation

If the coin is fair, the probability of getting more than two-thirds tails in 90 flips is 0.0008. This is much smaller than the usual 0.05 cutoff, so such a result would be very unlikely to occur by chance if the coin were fair. It is therefore convincing evidence against the claim that the coin is fair. Choice A states this reasoning.

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