When two births are randomly selected, the sample space for genders is bb, bg, g

Question

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. Determine the probabilities of each sample proportion.

Sample proportion of girls                                                     Probability

0                                                                                               ______

0.25                                                                                          ______

0.75                                                                                          ______

(Type integers or simplified fractions.)

Explanation / Answer

If we represent boy by B and girl by G then for two births, the sample space will be:

{BB, BG, GB, GG}

So,

Sample proportion of girls with probabilities will be:

Mean of sample proportions = 0(1/4) + 0.5(1/2) + 1(1/4) = 1/2 = 0.5

Yes,

The results suggest that sample proportion is an unbiased estimator of a population proportion.

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