correlation between confidence level & width of interval

Title

• $\uparrow$ confidence level = $\uparrow$ width of interval
  • higher confidence level = we want to be more confident in our population parameter prediction = must allow more data variability = wider range of interval
  • width of confidence is determined by $2\cdot z_{\frac{\alpha }{2}}\frac{\sigma }{\sqrt{n}}$ = 2 times the margin of error. As confidence level $\uparrow$→ z-score $\uparrow$ → wider width