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 5, the probability of having a girl is 5, 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 (Type integers or simplified fractions.) Does the mean of the sample proportions equal the proportion of girls in two births? O A. No, the mean of the sample proportions and the population proportion are not equal. O B. Yes, both the mean of the sample proportions and the population proportion are OC. Yes, both the mean of the sample proportions and the population proportion are a OD. Yes, both the mean of the sample proportions and the population proportion are Does the result suggest that a sample proportion is an unbiased estimator of a population proportion? OA. Yes, because the sample proportions and the population proportion are the same. OB. Yes, because the sample proportions and the population proportion are not the same O C. No, because the sample proportions and the population proportion are the same. OD. No, because the sample proportions and the population proportion are not the same

Answer 1

since there are total 2^3 =8 samples, therefore each sample occur with probability of 1/8

sample proportion			probability
0			1/4
0.5			1/2
1			1/4

OB. Yes, both the mean of the sample proportions and the population proportion are

O A. Yes, because the sample proportions and the population proportion are the same