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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 probability misinterpretation?
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As noted, "the probability pp is in this interval" is wrong. Use the long-run-procedure language.
What is sample size not rounded up?
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n=383.1n = 383.1 becomes n=384n = 384, not 383383.
What is worst-case p^\hat{p} ignored?
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If a study design problem gives no prior estimate of pp, the worst-case p^=0.5\hat{p} = 0.5 should be used to ensure the margin is met regardless.
What is standard error with pp instead of p^\hat{p}?
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Use p^\hat{p} in the CI standard error; pp is unknown.
What is q1?
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A sample of 250250 has p^=0.4\hat{p} = 0.4. Find the standard error. [2 marks]
What is q2?
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From 600600 items, 9090 are faulty. Construct a 95%95\% confidence interval for the true fault rate. [3 marks]
What is q3?
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State why "there is a 95% probability the true proportion lies in (0.121, 0.179)" is an incorrect interpretation. [2 marks]

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