A researcher wants to estimate the proportion of city...

A researcher wants to estimate the proportion of city residents who favor spending city funds to promote tourism. Would the standard error of the sample proportion $\hat{p}$ be smaller for random samples of size $n=100$ or random samples of size $n=200 ?$

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Key Concepts

Effect of Sample Size on Standard Error

Sample size directly influences the standard error; as the sample size increases, the standard error decreases. This relationship, often encapsulated by the formula sqrt(p(1-p)/n) for proportions, indicates that larger samples yield more precise estimates of a population parameter.

Estimation of Proportions

Estimating proportions involves using sample data to infer the percentage of a population that exhibits a certain characteristic. This process relies on probability theory and the properties of the sampling distribution, making it a fundamental aspect of survey analysis and inferential statistics.

Standard Error

The standard error quantifies the variability of an estimator, measuring the extent to which the sampled statistic (like a proportion) varies from sample to sample. It’s a crucial concept in statistical inference as it provides insight into the reliability and precision of the estimate.

Sampling Distribution of the Proportion

This is the probability distribution of the sample proportion calculated from repeated random samples drawn from the same population. It forms the basis of making inferences about the population proportion and is essential for constructing confidence intervals and conducting hypothesis tests.

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