A simple random sample of 3,500 people age 18 or over is...

A simple random sample of $3,500$ people age 18 or over is taken in a large town to estimate the percentage of people (age 18 and over in that town) who read newspers. It turns out that $2,487$ people in the sample are newspaper readers. 12 The population percentage is estimated as $$ \frac{2,487}{3,500} \times 100 \% \approx 71 \% $$ The standard error is estimated as 0.8 of $1 \%,$ because $$ \sqrt{3,500} \times \sqrt{0.71 \times 0.29} \approx 27, \quad \frac{27}{3,500} \times 100 \% \approx 0.8 \text { of } 1 \% $$ $$ \begin{array}{l}{\text { (a) Is } 0.8 \text { of } 1 \% \text { the right SE? Answer yes or no, and explain. }} \\ {\text { (b) } 71 \% \pm 1.6 \% \text { is a }}\end{array} $$

A simple random sample of $3,500$ people age 18 or over is taken in a large
town to estimate the percentage of people (age 18 and over in that town) who
read newspers. It turns out that $2,487$ people in the sample are newspaper
readers. 12 The population percentage is estimated as
$$
\frac{2,487}{3,500} \times 100 \% \approx 71 \%
$$
The standard error is estimated as 0.8 of $1 \%,$ because
$$
\sqrt{3,500} \times \sqrt{0.71 \times 0.29} \approx 27, \quad \frac{27}{3,500} \times 100 \% \approx 0.8 \text { of } 1 \%
$$
$$
\begin{array}{l}{\text { (a) Is } 0.8 \text { of } 1 \% \text { the right SE? Answer yes or no, and explain. }} \\ {\text { (b) } 71 \% \pm 1.6 \% \text { is a }}\end{array}
$$

Key Concepts

Simple Random Sampling

Simple random sampling is a fundamental sampling method where every member of the population has an equal chance of being selected. This technique minimizes bias and ensures that the sample is representative of the population, which is essential for reliable statistical inference.

Population Proportion Estimation

Population proportion estimation involves using the sample proportion to infer the proportion of the entire population that exhibits a particular characteristic. This concept is central to survey analysis and helps in making generalizations about the population based on the sample data.

Standard Error of a Sample Proportion

The standard error for a sample proportion quantifies the variability of the sample proportion as an estimator for the true population proportion. It is calculated using the sample size and the estimated proportion, and it plays a critical role in determining the reliability of the estimation and constructing confidence intervals.

Confidence Interval

A confidence interval provides a range of plausible values for the population parameter, calculated by adding and subtracting a margin of error from the point estimate. It reflects not only the estimate from the sample but also the uncertainty associated with sampling variability, allowing for probabilistic statements about the population proportion.

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