In survey research, why are the minor statistical gains from surveying significantly more than 1,000 people generally not considered worth the additional time and financial cost?

A researcher studying a population of 100 million people requires a significantly larger sample size to achieve a 95% confidence interval than a researcher studying a population of 100,000 people.

Match each research scenario with the appropriate statistical reasoning regarding the relationship between sample and population size.

A team of researchers is planning a national survey. They are analyzing how various adjustments to their study design will influence the precision (width) of their 95% confidence interval.

Arrange the following modifications in order from the one that produces the LARGEST reduction in the width of the confidence interval to the one that produces the SMALLEST (or zero) reduction.

In survey research, a $95\%$ confidence interval depends only on the size of the sample itself, not on the size of the population.

A psychology researcher is planning a survey and considering whether to recruit $5,000$ participants instead of the typical $1,000$. According to the principles of sample size, how would surveying the additional $4,000$ people affect the confidence interval?

A research committee is evaluating the statistical rigor of two survey designs: Design A uses a sample of $1,000$ for a population of $100,000$, and Design B uses a sample of $1,000$ for a population of $100$ million. Based on the relationship between sample and population size, the committee should judge the precision of the resulting $95\%$ confidence intervals to be approximately _____.

A research team is hired to estimate voter preferences in a state with $4,000,000$ registered voters. They determine that surveying $1,000$ voters provides an acceptable $95\%$ confidence interval. If the team is later hired to run the exact same survey in a neighboring state with $12,000,000$ registered voters and wants the exact same level of precision, they should plan to survey approximately _____ voters.

Match each observed survey phenomenon or research decision to the underlying statistical principle that best explains it.

A university research committee is evaluating the methodological and financial justifications for four survey research proposals. All four proposals aim to estimate the prevalence of a psychological behavior in a national population of $300$ million people. The committee's primary goal is to endorse the proposal that achieves an adequate $95\%$ confidence interval without wasting research funds on progressively slower statistical gains.

Based on the relationship between sample size, population size, and statistical confidence, arrange the following proposed sample designs in order from the MOST justifiable (highest endorsement for efficiency) to the LEAST justifiable (lowest endorsement due to extreme waste for negligible gains).