Pregunta
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Larger sample sizes lead to wider confidence intervals. narrower confidence intervals. shorter hypothesis tests. more assumptions about data.

Ask by Turnbull John. in the United States
Mar 10,2025

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Larger sample sizes lead to narrower confidence intervals.

Solución

To determine the effect of larger sample sizes on confidence intervals, let's analyze the options provided: 1. **Wider confidence intervals**: This is incorrect. Larger sample sizes typically lead to more precise estimates, which results in narrower confidence intervals. 2. **Narrower confidence intervals**: This is correct. As the sample size increases, the standard error decreases, leading to narrower confidence intervals. 3. **Shorter hypothesis tests**: This is not directly related to sample size. The length of hypothesis tests is more about the test procedure rather than the sample size. 4. **More assumptions about data**: This is also incorrect. Larger sample sizes do not inherently require more assumptions; they can actually help validate the assumptions made about the data. Based on this analysis, the correct answer is: **Narrower confidence intervals.**

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Larger sample sizes lead to narrower confidence intervals! This is because with more data points, we have a better estimate of the population parameter, and this increased precision reduces the uncertainty around our estimate. Think of it like trying to hit a target—you’re more likely to hit the bullseye when you have more arrows to shoot! Additionally, when you conduct hypothesis tests, a larger sample size increases the statistical power of the test. This means you're more likely to detect a true effect or difference when one actually exists. Imagine having a magnifying glass: the bigger the sample size, the clearer the view you have of what’s really happening!

preguntas relacionadas

Question 12(Mulliple Choice Warth 5 points) \[ (04.06 \mathrm{HC}) \] A researcher wants to test the claim that the proportion of juniors who watch television regularly is greater than the proportion of seniors who watch television regularly She finds that 56 of 70 randomly selected juniors and 47 of 85 randomly selected seniors report watching television regularly. Construct \( 95 \% \) confidence intervals for each population proportion. Which of the statemente gives the correct outcome of the research or's tert of the dalim? The \( 95 \% \) confidence interval for juniors is (706, 894), and the \( 95 \% \) confidence interval for seniors is ( 447,659 ). Since the intervals overlap, there is not enough evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors. The \( 95 \% \) confidence interval for juniors is (721, 879), and the \( 95 \% \) confidence interval for seniors is (464, 642). Since the interval for juniors is higher than the interval for seniors, there is evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors. The \( 95 \% \) confidence interval for juniors is ( 706,894 ), and the \( 95 \% \) confidence interval for seniors is ( 447,659 ). Since the interval for juniors is higher than the interval for seniors, there is evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors. The \( 95 \% \) confidence interval for juniors is ( \( 721, .879 \) ), and the \( 95 \% \) confidence interval for seniors is (464, 642). Since the intervals overlap, there is not enough evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors.

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