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? Fotheentire population, assume the probability of having a boy is , the probability of having a gil is 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? OA. Yes, both the mean of the sample proportions and the population proportion are OB. Yes, both the mean of the sample proportions and the population proportion are 3 O C. No, the mean of the sample proportions and the population proportion are not equal. 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 not the same O B. No, because the sample proportions and the population proportion are the same. C. Yes, because the sample proportions and the population proportion are the same ( D. No, because the sample proportions and the population proportion are not the same.

Explanation / Answer

When two births are randomly selected, the sample space is: {bb, bg, gb, gg}

Table for sampling distribution of sample proportions

X

0

1

2

P(x)

0.25

0.50

0.25

The probability of each sample proportion

Sample proportion of girls probability

0 / 2 = 0 0.25

1 / 2 = 0.5 0.50

2 / 2 = 1 0.25

Mean of distribution is = 0*0.25+1*0.50+2*0.25 = 1

Mean of proportion of girls in two births = 0*0.25+0.5*0.50+1*0.25 = 0.5

Correct option is C. No, the mean of the sample proportions and population proportion are not equal.

Correct option is C

X

0

1

2

P(x)

0.25

0.50

0.25

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