Keypoints

• You learned to calculate confidence intervals for a sample mean and sample proportion.
• For both confidence intervals you need to calculate standard errors, and for both you need to calculate critical values from the relevant probability distribution (t-distribution for a mean, z-distribution for a proportion).
• Confidence interval for a mean: #\overline{x}-t_{\alpha/2}\cdot se_{\overline{x}}\le\mu\le\overline{x}+ t_{\alpha/2}\cdot se_{\overline{x}}#
  with #se_{\overline{x}}= s/\sqrt{n}# (no need to memorize - equations are provided on formula sheet)
• Confidence interval for a proportion: #\hat{p}-z_{\alpha/2}\cdot se_{\hat{p}}\le p\le \hat{p}+z_{\alpha/2}\cdot se_{\hat{p}}#
  with #se_{\hat{p}}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}# (no need to memorize - equations are provided on formula sheet)
• If a sample size gets bigger, the confidence interval becomes narrower.
• If the confidence level gets higher, the confidence interval becomes wider.