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A test of a proportion

A hypothesis test asks whether the data give enough reason to reject a claim. The null hypothesis is the claim of no change, here that the coin is fair. The test statistic compares the observed count with what the null hypothesis expects, and divides by the standard deviation under the null hypothesis. The course normal table gives the p-value 1 minus Φ of 2, about 0.023. That value is looked up, not calculated with the four operations. A one-sided 5% test rejects when Z is greater than the table value 1.645.

Symbols

Example

60 heads in 100 tosses, $H_0: p = 0.5$.

$Z = \dfrac{60 - 50}{\sqrt{100 \cdot 0.5 \cdot 0.5}} = \dfrac{10}{5} = 2$.

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Part of Mathematics S2: Hypothesis testing.