SOLUTION: When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg. Assume that those four outcomes are equally likely. Construct a table that descr
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Question 1168625: When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion is an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is 1/2
, the probability of having a girl is 1/2
, and this is not affected by how many boys or girls have previously been born.
I have no clue how or what to do here.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
BB proportion 1/4
BG proportion 1/4
GB proportion 1.4
GG proportion 1/4
E(X) where x is number of girls expected from 2 births. It is the sum of all the random variables x*p(x)
=0*1/4=1/(1/4)+1(1/4)+2 (1/4)=1
So the mean number of girls in 2 births is 1.
This suggests that the sample proportion is an unbiased estimate of the population proportion, because the expected value is the same as the population proportion (1/2) and 1 girl in 2 pregnancies.
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