Sample Size and Population Size
In survey research, a sample of about individuals is typically considered adequate to make accurate estimates, regardless of whether the broader population consists of a hundred thousand or a hundred million people. This is because a confidence interval depends only on the size of the sample itself, not on the size of the population. Furthermore, while increasing the sample size continues to shrink the confidence interval—meaning the sample statistic is likely closer to the true population value—it does so at a progressively slower rate. Consequently, the minor gains in statistical confidence achieved by surveying significantly more than people are generally not considered worth the additional time and financial cost.
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Research Methods in Psychology - 4th American Edition @ KPU
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Confidence Interval
Sample Size and Population Size
When determining the optimal sample size for a survey, what are the two primary factors a researcher must generally balance?
A psychology researcher is planning a survey to study community health habits. Match each factor involved in determining their sample size with the specific role it plays in the planning process.
A social psychologist planning a survey on community resilience determines that 900 participants are required to achieve their desired level of statistical confidence. However, after realizing that the recruitment costs for 900 people would exceed their $500 research grant, they decide to survey only 400 people. In this scenario, the researcher has prioritized the study's budget over their initial goal for statistical confidence.
A psychology researcher is planning a survey on community mental health. Arrange the following steps in the logical sequence required to analyze and balance the determinants of their study's sample size.
When determining survey sample size, researchers frequently use a power analysis to balance the desired level of statistical confidence with the practical constraints of their study's budget.
When planning a survey, a researcher must understand how sample size relates to both statistical confidence and practical constraints. Which statement best describes the trade-off a researcher faces when determining their survey's sample size?
A psychology researcher finds that increasing their survey sample from to participants would cost an additional $1,500 but only provide a negligible increase in statistical confidence. By deciding that the marginal gain in precision does not justify the extra expense, the researcher has performed a/an _____ of the trade-off between the study's theoretical goals and its practical budget constraints.
A research methods instructor asks students to apply their understanding of survey sample size principles to concrete research situations. Match each scenario to the principle of survey sample size determination it best illustrates.
A researcher plans a large-scale health survey and determines through a power analysis that 1,000 participants are needed to reach her desired level of statistical confidence. After reviewing her grant award, she discovers she can only afford 400 participants. By breaking down what is preventing her from achieving her ideal sample size, a careful reviewer would conclude that the binding determinant in this scenario is the study's _____.
A research methods instructor asks students to critically evaluate whether a researcher made well-justified decisions when determining her survey sample size. Arrange the following evaluative steps in the order that would allow a reviewer to reach the most defensible judgment about the appropriateness of the researcher's chosen sample size.
Sample Size and Population Size
Example of a Confidence Interval
By definition, a confidence interval is a statistical range calculated around a sample statistic that is designed to contain which of the following a specified percentage of the time?
If a calculated confidence interval completely excludes a specific hypothetical population mean, a researcher can conclude that the sample mean is not statistically significantly different from that hypothetical value.
A cognitive psychologist is testing a new training method to determine its effect on reaction times. The average reaction time in the general population is known to be 400 milliseconds (ms). Match each of the following research results (presented as 95% Confidence Intervals) to the correct statistical conclusion regarding the training group's performance.
A researcher is analyzing the results of a psychological study and determines that the confidence interval is too wide to be useful. Arrange the following steps in the logical order that describes how the researcher's decision to increase the sample size leads to a more precise estimate.
A developmental psychologist is designing a mock-up of a research poster to teach students how to evaluate statistical findings. The goal is to create a hypothetical scenario where a new intervention's impact is judged to be 'statistically effective' compared to a baseline population mean of , but where the specific estimate of that impact remains highly uncertain (represented by a wide range). Which of the following result summaries should the psychologist construct to fulfill these specific design goals?
The most commonly used confidence interval in psychological research is set to contain the true population parameter of the time.
A student in an introductory psychology research methods course is learning about interval estimation. Match each component or outcome of a confidence interval with its correct conceptual interpretation.
A clinical psychologist is evaluating a claim that a specific mindfulness technique has no impact on stress levels (where a difference of indicates no impact). The researcher's study results in a confidence interval for the mean reduction in stress of . Because the value representing 'no impact' falls entirely outside this interval, the researcher should judge the initial claim as _____.
A social psychologist surveys 200 college students about daily social media use (in minutes) and obtains a confidence interval of [85, 115]. After examining the interval, the researcher notes that a media organization's claimed population mean of 130 falls completely _____ the interval, while a second published estimate of 95 falls completely inside it — leading the researcher to conclude that only the first claim is statistically refuted at the .05 level.
An undergraduate student completing a research methods paper must decide whether to report statistical results using only a null hypothesis test (p-value) or a confidence interval. Arrange the following steps of the student's evaluative reasoning in the most logical order.
Learn After
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 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 participants instead of the typical . According to the principles of sample size, how would surveying the additional people affect the confidence interval?
A research committee is evaluating the statistical rigor of two survey designs: Design A uses a sample of for a population of , and Design B uses a sample of for a population of million. Based on the relationship between sample and population size, the committee should judge the precision of the resulting confidence intervals to be approximately _____.