Sample Mean Distribution (AQA A-Level Mathematics): Flashcards

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Sample Mean Distribution
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Distribution of sample mean Xˉ\bar{X} (sample size nn, XN(μ,σ2)X \sim N(\mu, \sigma^2))

XˉN(μ,σ2n)\bar{X} \sim N(\mu, \frac{\sigma^2}{n})

What H0H_0 represents in hypothesis testing

No change in parameter/default position

H1:μ5H_1: \mu \neq 5 indicates what type of test?

Two-tailed test

Define critical/rejection region

Region where observation leads to rejecting H0H_0

Two-tailed test at 5% sig: % at each tail?

2.5%

Value of μ\mu to use in distribution when testing

Value from H0H_0

What is a p-value?

Probability of observing value (or more extreme) under H0H_0

Critical region method: reject H0H_0 when?

Observed value falls in critical region

Probability method: reject H0H_0 when?

Probability < significance level

Symbol for defining parameter in hypothesis test

μ\mu, not xˉ\bar{x}

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