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VICMath MethodsQuick questions
Unit 4
Quick questions on Confidence intervals for a population proportion: VCE Math Methods Unit 4
7short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is note. $\hat{p}$ vs $p$ in the standard error?Show answer
In the sampling-distribution formula, $\text{SD}(\hat{p}) = \sqrt{p(1-p)/n}$ uses the true (and usually unknown) $p$.
What is common misstatements VCAA marks against?Show answer
These are widespread but incorrect:
What is worst-case sample size?Show answer
If no prior estimate of $\hat{p}$ is available, use $\hat{p} = 0.5$ in the design formula, which maximises $\hat{p}(1 - \hat{p}) = 0.25$. This gives the largest required $n$ and so a conservative design.
What is probability misinterpretation?Show answer
As noted, "the probability $p$ is in this interval" is wrong. Use the long-run-procedure language.
What is sample size not rounded up?Show answer
$n = 383.1$ becomes $n = 384$, not $383$.
What is worst-case $\hat{p}$ ignored?Show answer
If a study design problem gives no prior estimate of $p$, the worst-case $\hat{p} = 0.5$ should be used to ensure the margin is met regardless.
What is standard error with $p$ instead of $\hat{p}$?Show answer
Use $\hat{p}$ in the CI standard error; $p$ is unknown.
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