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population, assume the probability ng a boy is , the probability of having a girl is , and this is not affected by how many boys or girls have previously been bon. mine the probabilities of each sample proportion. Sample proportion of girls Probability Type integers or simplified fractions. s the mean of the sample proportions equal the proportion of girls in two births? A. Yes, both the mean of the sample proportions and the population proportion are B. No, the mean of the sample proportions and the population proportion are not equal. OC. Yes, both the mean of the sample proportions and the population proportion are - D. 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 No, because the sample proportions and the population proportion are the same. Textbook StatGrunch

population, assume the probability ng a boy is , the probability of having a girl is , and this is not affected by how many boys or girls have previously been bon. mine the probabilities of each sample proportion. Sample proportion of girls Probability Type integers or simplified fractions. s the mean of the sample proportions equal the proportion of girls in two births? A. Yes, both the mean of the sample proportions and the population proportion are B. No, the mean of the sample proportions and the population proportion are not equal. OC. Yes, both the mean of the sample proportions and the population proportion are - D. 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 No, because the sample proportions and the population proportion are the same. Textbook StatGrunch

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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The image presents an educational exercise about probability and sampling distribution. Here is a transcription and explanation suitable for an educational website: --- **Exercise: Sampling Distribution of Sample Proportions** When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg. 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. 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 \( \frac{1}{2} \). The probability of having a girl is also \( \frac{1}{2} \), 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 | |----------------------------|-------------| | | | | | | | | | *(Type integers or simplified fractions)* **Questions:** 1. **Does the mean of the sample proportions equal the proportion of girls in two births?** - A. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{4} \). - B. No, the mean of the sample proportions and the population proportion are not equal. - C. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{3} \). - D. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{2} \). 2. **Does the result suggest that a sample proportion is an unbiased estimator of a population proportion?** - A. No, because the sample proportions and the population proportion are the same. **Tools Provided:** - Textbook - StatCrunch --- In this activity, learners are prompted to fill in the probability table and answer questions about the relationship between sample proportions and population proportions. The goal is to understand the concept of unbiased estimation in probability and statistics.
Transcribed Image Text:The image presents an educational exercise about probability and sampling distribution. Here is a transcription and explanation suitable for an educational website: --- **Exercise: Sampling Distribution of Sample Proportions** When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg. 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. 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 \( \frac{1}{2} \). The probability of having a girl is also \( \frac{1}{2} \), 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 | |----------------------------|-------------| | | | | | | | | | *(Type integers or simplified fractions)* **Questions:** 1. **Does the mean of the sample proportions equal the proportion of girls in two births?** - A. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{4} \). - B. No, the mean of the sample proportions and the population proportion are not equal. - C. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{3} \). - D. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{2} \). 2. **Does the result suggest that a sample proportion is an unbiased estimator of a population proportion?** - A. No, because the sample proportions and the population proportion are the same. **Tools Provided:** - Textbook - StatCrunch --- In this activity, learners are prompted to fill in the probability table and answer questions about the relationship between sample proportions and population proportions. The goal is to understand the concept of unbiased estimation in probability and statistics.
## Educational Content: Analyzing Proportions in Statistics ### Understanding Sample and Population Proportions Consider the following exercise: **Question 1:** Does the mean of the sample proportions equal the proportion of girls in two births? - **A.** Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{4} \). - **B.** No, the mean of the sample proportions and the population proportion are not equal. - **C.** Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{3} \). - **D.** Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{2} \). *Correct Answer: D. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{2} \).* **Question 2:** Does the result suggest that a sample proportion is an unbiased estimator of a population proportion? - **A.** No, because the sample proportions and the population proportion are the same. - **B.** Yes, because the sample proportions and the population proportion are not 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. *Correct Answer: C. Yes, because the sample proportions and the population proportion are the same.* ### Explanation These questions explore the concept of sample proportions as unbiased estimators of population proportions. The exercise demonstrates that, when samples are drawn appropriately, the mean of the sample proportions should ideally reflect the true population proportion, affirming the reliability of statistical estimation methods.
Transcribed Image Text:## Educational Content: Analyzing Proportions in Statistics ### Understanding Sample and Population Proportions Consider the following exercise: **Question 1:** Does the mean of the sample proportions equal the proportion of girls in two births? - **A.** Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{4} \). - **B.** No, the mean of the sample proportions and the population proportion are not equal. - **C.** Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{3} \). - **D.** Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{2} \). *Correct Answer: D. Yes, both the mean of the sample proportions and the population proportion are \( \frac{1}{2} \).* **Question 2:** Does the result suggest that a sample proportion is an unbiased estimator of a population proportion? - **A.** No, because the sample proportions and the population proportion are the same. - **B.** Yes, because the sample proportions and the population proportion are not 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. *Correct Answer: C. Yes, because the sample proportions and the population proportion are the same.* ### Explanation These questions explore the concept of sample proportions as unbiased estimators of population proportions. The exercise demonstrates that, when samples are drawn appropriately, the mean of the sample proportions should ideally reflect the true population proportion, affirming the reliability of statistical estimation methods.
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