Question

All of Kate’s children are boys.

1. Intuitively, how many boys do you think Kate would have to have in succession before you would be willing to say with some cer- tainty that, for some biological reason, she is more likely to give birth to boys than girls?

2. Now calculate the number of successive births required before you could make such a decision statistically with a 5% risk of error.

3. How many successive boys would have to be born before you would be prepared to come to this conclusion with only a 1% risk of error?

Answer 1

a) Intuitively I will say if there are 4 consecutive boys then I can conclude that for some biological reason, she is more likely to give birth to boys than girls. This is because the occurrence of this even has a probability 0.0625 which is very low.

b) Here we want to find "b" such that P(X=b)<0.05, then b=5. as P(X=5)=0.03125 i.e. probability of 5 consecutive births is 0.03125.

c) Here we want to find "b" such that P(X=b)<0.01, then b=7. as P(X=7)=0.015625 i.e. probability of 7 consecutive births is 0.015625.