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A polling organization plans to ask a random sample of likely voters who they plan to vote for in an upcoming election. The researchers will report the sample proportion hat (p) that favors the incumbent as an estimate of the population proportion p that favors the incumbent. What does it mean to say that hat (p) is an unbiased estimator of p? This means that the sample proportion will overestimate the population proportion when the distribution is skewed to the right and will underestimate the population proportion when the distribution is skewed to the left. This means that the proportion of the population will always be close to the value of the sample proportion. If we select an SRS and calculated the sample proportion, the sample proportion will equal the population proportion. If we chose many SRSs and calculated the sample proportion hat (p) for each sample, the distribution of hat (p) would be centered at the value of p

Problemas

A polling organization plans to ask a random sample of likely voters who they plan to vote for in an upcoming election. The researchers will report the sample proportion hat (p) that favors the incumbent as an estimate of the population proportion p that favors the incumbent. What does it mean to say that hat (p) is an unbiased estimator of p? This means that the sample proportion will overestimate the population proportion when the distribution is skewed to the right and will underestimate the population proportion when the distribution is skewed to the left. This means that the proportion of the population will always be close to the value of the sample proportion. If we select an SRS and calculated the sample proportion, the sample proportion will equal the population proportion. If we chose many SRSs and calculated the sample proportion hat (p) for each sample, the distribution of hat (p) would be centered at the value of p

A polling organization plans to ask a random sample of likely voters who they plan to vote for in an upcoming election. The researchers will report the sample proportion hat (p) that favors the incumbent as an estimate of the population proportion p that favors the incumbent. What does it mean to say that hat (p) is an unbiased estimator of p? This means that the sample proportion will overestimate the population proportion when the distribution is skewed to the right and will underestimate the population proportion when the distribution is skewed to the left. This means that the proportion of the population will always be close to the value of the sample proportion. If we select an SRS and calculated the sample proportion, the sample proportion will equal the population proportion. If we chose many SRSs and calculated the sample proportion hat (p) for each sample, the distribution of hat (p) would be centered at the value of p

Solución

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Dinamaestro · Tutor durante 5 años
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To say that $\hat {p}$ is an unbiased estimator of p means that the expected value of the sample proportion $\hat {p}$ is equal to the population proportion p. In other words, if we were to take many random samples and calculate the sample proportion for each sample, the average of these sample proportions would be equal to the population proportion p.<br /><br />The correct answer is: If we chose many SRSs and calculated the sample proportion $\hat {p}$ for each sample, the distribution of $\hat {p}$ would be centered at the value of p.
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