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

$\bar{X} \sim N(\mu, \sigma^2/n)$ where $\sigma^2$ is known and $n$ is sample size.

$\bar{X} \sim N(100, 7^2/60)$

Use $Z = (102-100)/7$; $P(Z > 0.2857)$ from Z-table.

It represents the probability of the mean being over $102$.

$H_0: \mu = 21$, $H_1: \mu > 21$

It identifies values that reject the null hypothesis.

$P(\bar{X} > 21.2) = 0.2755$

It indicates insufficient evidence to reject $H₀$.

H₀: $\mu = 5$, H₁: $\mu \neq 5$

Reject $H_0$: Mean is significantly different from $5$.