According to my null hypothesis we should see responses from an equal number of responses from first-of-two and second-of-two people. So the question we need to ask is: If I take 18 people who grew up with exactly one other sibling and each is 50-50 to be the eldest, what is the probability that 3 or fewer from my sample are youngest?
This probability is (I claim): (0.5^3 x 0.5^15 x 18C3) + (0.5^2 x 0.5^16 x 18C2) + (0.5^1 x 0.5^17 x 18C1) + (0.5^0 x 0.5^18 x 18C0)
This simplifies in an obvious way to: 0.5^18 x (18C3 + 18C2 + 18C1 + 18C0)
Because I'm lazy, I just Googled for a big picture of Pascal's triangle and pulled the last four digits off the 18th row without checking them. They are (allegedly): 680, 136, 17 and 1.
So our probability is (680 + 136 + 17 + 1) / 2^18.
Which is 834 / 262144.
This is approximately 1/314.
(Feel free to poke holes in this - it's been well over 15 years since I last did this stuff and I may have messed it up!)
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According to my null hypothesis we should see
responses froman equal number of responses from first-of-two and second-of-two people. So the question we need to ask is: If I take 18 people who grew up with exactly one other sibling and each is 50-50 to be the eldest, what is the probability that 3 or fewer from my sample are youngest?This probability is (I claim): (0.5^3 x 0.5^15 x 18C3) + (0.5^2 x 0.5^16 x 18C2) + (0.5^1 x 0.5^17 x 18C1) + (0.5^0 x 0.5^18 x 18C0)
This simplifies in an obvious way to: 0.5^18 x (18C3 + 18C2 + 18C1 + 18C0)
Because I'm lazy, I just Googled for a big picture of Pascal's triangle and pulled the last four digits off the 18th row without checking them. They are (allegedly): 680, 136, 17 and 1.
So our probability is (680 + 136 + 17 + 1) / 2^18.
Which is 834 / 262144.
This is approximately 1/314.
(Feel free to poke holes in this - it's been well over 15 years since I last did this stuff and I may have messed it up!)