I Give You a Coin, and You Flip It 100

question 14

Multiple Choice

I give you a coin, and you flip it 100 times. Let X = the number of heads observed in those 100 flips. You build the following line of reasoning:
Steps
1) You assume each flip is an independent, random outcome.
2) You assume the coin is fair.
3) Using your statistics book, you conclude that X is distributed binomial with mean 50 and variance 25.
4) Based on this distribution, you conclude that you would observe X < 41 or X > 59 approximately 5% of the time.
5) You observe X = 37 and conclude that the probability that X < 41 or X > 59 is not 5%.
6) Because the probability that X < 41 or X > 59 is not 5%, you conclude the coin is not fair.
Which of these steps is part of deductive reasoning?

• A) Steps 1, 2, 3, 4, and 6 only
• B) Steps 4 and 6 only
• C) All 6 steps
• D) Steps 3, 4, and 5 only

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