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# Test the hypothesis

Posted on 2006-12-01

Birth records were collected from the first 5 births in 51,868 families to test that the gender of successive off-spring are independent.

In families with exactly 5 children, the following is a frequency distribution of male offspring.

Number of Male Offspring N

0 518

1 2245

2 4621

3 4753

4 2476

5 549

Total 15,162

Suppose we doubt that the probability of male birth is exactly 50%, but are willing to assume that the gender of successive offspring are independent.

What is the best estimate of the probability of a male birth based on the observed data?

What is the probability of 0, 1, 2, 3, 4, and 5 male births out of 5 births based on the estimate obtained.

How do we test the hypothesis that the gender of successive offspring are independent based on the model above.

thx

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