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QLDMath MethodsQuick questions

Unit 4: Further calculus and statistical inference

Quick questions on Sample proportions and confidence intervals: QCE Maths Methods Unit 4

5short 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 mean?
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E(p^)=pE(\hat{p}) = p. The sample proportion is an unbiased estimator of pp.
What is standard deviation?
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SD(p^)=p(1−p)n\text{SD}(\hat{p}) = \sqrt{\frac{p(1-p)}{n}}.
What is sample size economics?
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Doubling nn reduces SE by a factor of 2\sqrt{2}. Quadrupling nn halves SE. Diminishing returns above n≈1000n \approx 1000 for opinion polling.
What is probability misinterpretation?
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"The probability pp is in this interval" is wrong. Use long-run-procedure language.
What is sample size not rounded up?
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n=384.1n = 384.1 becomes n=385n = 385, not 384.

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