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May 28th, 2011, 10:14 AM  #1 
Newbie Joined: Dec 2009 Posts: 2 Thanks: 0  Probability of gender determination
It is often stated in Biology that the probability of a a baby being a boy is 0.5 (and a girl 0.5). However there are instances of couples having a sequence of boys (or girls), sometimes 5, 6 or 7 children. For this couple, is P(boy)=0.5 or p>0.5? If I consider 5 boys out of 6 children, as a hypothesis test (to 5% SL) H0:P=0.5 H1:P>0.5 P(X=<5) = 0.984, therefore to 5% would reject H0 and accept H1. To 95% confidence there is evidence that P>0.5. Does this contradict the idea that the P=0.5 for all couples, at every sample? Thanks Stuart 
May 28th, 2011, 07:35 PM  #2 
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Probability of gender determination
I don't know where the .984 came from  it's a small sample size and I don't know how to do a small sample for a proportion. But there's a couple of comments I could make. You can get a sample in that rejection range and it doesn't mean the original hypothesis is false. There can be error involved. If you're 95% confidence, there's also 5% chance you're wrong. That 5% exists. Second, this isn't a random sample  it's a particular set of parents. Another set of parents could have 5 girls out of 6 children. But if the probability of having a boy is indeed .5 (not sure it is), then for each individual child born, it's still .5. (And this is not taking into account whatever biological things could affect this.) I supposed you could say it contradicts the .5 for "all couples, at every sample," cause it's not like all couples and every sample will turn out that way, and we wouldn't expect it to. 
May 28th, 2011, 09:45 PM  #3 
Member Joined: May 2011 Posts: 51 Thanks: 0  Re: Probability of gender determination
Probability is before the event. It doesn't guarantee the outcome. Let's take a dice and write 6 on it's 5 sides, and on the 1 side left write 1. In every throw probability of 6 is 5/6 and probability of 1 is 1/6, but still the result can be 1 and that is not contradictory with the probability. Actually that is called Life I am a very hard working, dedicated, committed and loyal employee, but my colleague is the hotnewgirl friend of my boss. Now whatever way I calculate the probability of my promotion, that girl is gonna get promoted, and math. has nothing to do with it. 
June 4th, 2011, 04:33 PM  #4  
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Quote:
 

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