Population/Sample Proportions (Leaving Cert Mathematics): Flashcards

It's the fraction of the entire population with a characteristic.

$\hat{p} = \frac{x}{n}$ where $x$ is successes, $n$ is size.

$p$ is a fixed parameter; $\hat{p}$ varies between samples.

$\hat{p} \pm z \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

It represents the proportion of a sample with a characteristic.

'$z$' is the Z-value for the desired confidence level.

Use point estimates or confidence intervals from $\hat{p}$.

The sample proportion is $0.6$ or $60\%$.

The confidence interval is $(0.532, 0.668)$.

They help make predictions about populations from samples.