# Test the hypothesis

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

ej

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Commented:
15162 * (38395/75810)^0 * (1-38395/75810)^(5-0) * 5!/(0!*(5-0)!) = 443.969112662435
15162 * (38395/75810)^1 * (1-38395/75810)^(5-1) * 5!/(1!*(5-1)!) = 2277.98931988162
15162 * (38395/75810)^2 * (1-38395/75810)^(5-2) * 5!/(2!*(5-2)!) = 4675.31203725003
15162 * (38395/75810)^3 * (1-38395/75810)^(5-3) * 5!/(3!*(5-3)!) = 4797.7710990302
15162 * (38395/75810)^4 * (1-38395/75810)^(5-4) * 5!/(4!*(5-4)!) = 2461.71884735085
15162 * (38395/75810)^5 * (1-38395/75810)^(5-5) * 5!/(5!*(5-5)!) = 505.239583824862
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Commented:
38395 males / 75810 childern = 0.506
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Author Commented:
15162*5 = 75810

How do you get 38395?
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Commented:
0  * 518 +
1 * 2245 +
2 * 4621 +
3  * 4753 +
4  * 2476 +
5  * 549 +
= 38395
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Commented:
You might do a Chi-Square test of the hypothesis that the Number of Male Offspring follow a binomial distributon.
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Author Commented:
Why do you think 'Chi-Square test' for this data?
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Author Commented:
I got it.
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