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Quick questions on Hypothesis testing: null and alternative hypotheses, significance levels and critical regions - Edexcel A-Level Maths

3short 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 a strategy for any hypothesis test?
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Every test on the paper follows the same five steps. First, define the parameter and state H0H_0 and H1H_1, deciding whether the alternative is one-tailed or two-tailed from the wording. Second, state the distribution of the test statistic assuming H0H_0 is true, such as XB(n,p0)X \sim B(n, p_0). Third, calculate the probability of a result as extreme as, or more extreme than, the one observed (or find the critical region).
What is q1?
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State suitable hypotheses for a two-tailed test that a proportion has changed from 0.30.3. [2 marks]
What is q2?
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For XB(10,0.2)X \sim B(10, 0.2), H0:p=0.2H_0: p = 0.2, H1:p>0.2H_1: p > 0.2 at 5%5\%, you observe X=5X = 5. Given P(X5)0.0328P(X \ge 5) \approx 0.0328, state the conclusion. [3 marks]

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