Inference for Proportions¶

One-Sample z-test for Population Proportion¶

z-test for Population Proportion¶

Used to test whether the population proportion, $p$, has changed A random sample of $n$ individuals from the population with a sample proportion of $\hat{p}$ is used to try to prove the case

Conditions for A z-test for Population Proportion¶

• Items in the sample satisfy the independence condition
  • Random sampling/assignment
  • If without replacement, $n < 0.1N$

• Sample size is large enough such that sampling distribution is approximately a normal distribution

  • $np_0 \geq 10$
  • $n(1-p_0) \geq 10$
  • $p_0$ is the population proportion in the null hypothesis, $p = p_0$

• $z = \dfrac{statistics - parameter}{standard\ error\ of\ the\ statistic}$

• $standard\ error\ of\ the\ statistic = \sqrt{\dfrac{p_0(1-p_0)}n}$

Confidence Interval¶

$confidence\ interval = \hat{p} \pm z \cdot \sqrt{\dfrac{p_0(1-p_0)}n}$