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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 1 a sample proportion is an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is the probability of having a girl is 2 2' and this is not affected by how many boys or girls have previously been born. 1 Determine the probabilities of each sample proportion. Sample proportion of girls ▼ Does the mean of the sample proportions equal the proportion of girls in two births? CIT 1 both the mean of the sample proportions and the population proportion are Probability □ (Type integers or simplified fractions.)

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 1 a sample proportion is an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is the probability of having a girl is 2 2' and this is not affected by how many boys or girls have previously been born. 1 Determine the probabilities of each sample proportion. Sample proportion of girls ▼ Does the mean of the sample proportions equal the proportion of girls in two births? CIT 1 both the mean of the sample proportions and the population proportion are Probability □ (Type integers or simplified fractions.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Transcription for Educational Website** 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 ... **Question 1:** Does the mean of the sample proportions equal the proportion of girls in two births? - O A. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{2} \) - O B. No, the mean of the sample proportions and the population proportion are not equal. - O C. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{4} \) - O D. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{3} \) **Question 2:** Does the result suggest that a sample proportion is an unbiased estimator of a population proportion? - O A. No, because the sample proportions and the population proportion are the same. - O B. Yes, because the sample proportions and the population proportion are the same. - O C. Yes, because the sample proportions and the population proportion are not the same. - O D. No, because the sample proportions and the population proportion are not the same. **Note:** This exercise is aimed at understanding statistical concepts such as sample proportions, population proportions, and unbiased estimators. The answer selections explore the relationship between these statistical measures in the context of a simplified scenario of gender outcomes from births.
Transcribed Image Text:**Transcription for Educational Website** 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 ... **Question 1:** Does the mean of the sample proportions equal the proportion of girls in two births? - O A. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{2} \) - O B. No, the mean of the sample proportions and the population proportion are not equal. - O C. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{4} \) - O D. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{3} \) **Question 2:** Does the result suggest that a sample proportion is an unbiased estimator of a population proportion? - O A. No, because the sample proportions and the population proportion are the same. - O B. Yes, because the sample proportions and the population proportion are the same. - O C. Yes, because the sample proportions and the population proportion are not the same. - O D. No, because the sample proportions and the population proportion are not the same. **Note:** This exercise is aimed at understanding statistical concepts such as sample proportions, population proportions, and unbiased estimators. The answer selections explore the relationship between these statistical measures in the context of a simplified scenario of gender outcomes from births.
When two births are randomly selected, the sample space for genders is bb (both boys), bg (boy and girl), gb (girl and boy), and gg (both girls). Assume that these four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. For the entire population, assume the probability of having a boy is \( \frac{1}{2} \); similarly, the probability of having a girl is \( \frac{1}{2} \). This means the sample proportion is an unbiased estimator of a population proportion. **Table: Sampling Distribution** \[ \begin{array}{|c|c|} \hline \text{Sample Proportion of Girls} & \text{Probability} \\ \hline 0 & \\ \hline 0.5 & \\ \hline 1 & \\ \hline \end{array} \] **Question:** Does the mean of the sample proportions equal the proportion of girls in two births? - **Option A:** Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{2} \). - **Option B:** No, the mean of the sample proportions and the population proportion are not equal. Consider the logic of outcomes: In two births, getting bb results in 0 girls. Outcomes bg and gb both result in 1 girl each (or a 0.5 proportion). The gg outcome results in 2 girls (or a 1 proportion of girls). Therefore, calculate the probabilities based on this understanding to fill out the table and determine the correct answer.
Transcribed Image Text:When two births are randomly selected, the sample space for genders is bb (both boys), bg (boy and girl), gb (girl and boy), and gg (both girls). Assume that these four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. For the entire population, assume the probability of having a boy is \( \frac{1}{2} \); similarly, the probability of having a girl is \( \frac{1}{2} \). This means the sample proportion is an unbiased estimator of a population proportion. **Table: Sampling Distribution** \[ \begin{array}{|c|c|} \hline \text{Sample Proportion of Girls} & \text{Probability} \\ \hline 0 & \\ \hline 0.5 & \\ \hline 1 & \\ \hline \end{array} \] **Question:** Does the mean of the sample proportions equal the proportion of girls in two births? - **Option A:** Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{2} \). - **Option B:** No, the mean of the sample proportions and the population proportion are not equal. Consider the logic of outcomes: In two births, getting bb results in 0 girls. Outcomes bg and gb both result in 1 girl each (or a 0.5 proportion). The gg outcome results in 2 girls (or a 1 proportion of girls). Therefore, calculate the probabilities based on this understanding to fill out the table and determine the correct answer.
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