Hypothesis Testing and Errors (AQA A-Level Further Maths): Flashcards

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Hypothesis Testing and Errors
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Poisson parameter λ\lambda meaning

Average number of events in a fixed interval

Best estimate of λ\lambda from sample data

Sample mean

Null hypothesis (H0H_0) definition

Claim being tested; parameter equals specific value

Test statistic in Poisson hypothesis testing

Total number of events in the sample

Type I error definition

Rejecting a true null hypothesis (false positive)

Type II error definition

Accepting a false null hypothesis (false negative)

p-value definition

Probability of result as extreme as observed, if H0H_0 true

Decision rule using p-value

Reject H0H_0 if p-value < significance level

When to use one-tailed test

When interested if parameter increased OR decreased specifically

Type I error probability for discrete distributions

May be less than significance level (not exactly equal)

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