Confidence Interval Estimate for the Population Mean When the Population Variance Is Unknown

Statistics and Probability / Estimation of Parameters

Sample Question

What is the formula for finding the [% \left(1-\alpha\right)100\% %] confidence interval when the variance [% \left(\alpha^2 \right) %] is unknown?

  • [% \left[\overline{x}-t_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}},\overline{x}+t_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}\right] %]
  • [% \left[\overline{x}-z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}},\overline{x}+z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}\right] %]
  • [% \left[\overline{x}-t_{\frac{\alpha}{2}}\frac{s}{\sqrt{n}},\overline{x}+t_{\frac{\alpha}{2}}\frac{s}{\sqrt{n}}\right] %]
  • [% \left[\overline{x}-z_{\frac{\alpha}{2}}\frac{s}{\sqrt{n}},\overline{x}+z_{\frac{\alpha}{2}}\frac{s}{\sqrt{n}}\right] %]

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