Two-Sided Confidence Interval

^{Superscript text}A Two-Sided Confidence Interval is a confidence interval with an upper and lower bound.

• Example(s):
  • For N = $195$, Mean = $9.261460$, Standard Deviation = 0.022789, $t_{1-0.025,N-1} = 1.9723$, the Lower Limit = $9.261460 - 1.9723*0.022789/\sqrt{195}$ and Upper Limit = $9.261460 + 1.9723*0.022789/\sqrt{195}$. Thus, a 95 % confidence interval for the mean is $[9.258242, 9.264679]$.
  • ...
  • …
• Counter-Example(s):
  • One-Sided Confidence Interval.
• See: Statistical Test, Statistical Hypothesis, Statistical Estimation, T-test, Standard Deviation, Mean.

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References

2021a

• (NIST, 2021) ⇒ (2021). "Confidence Limits for the Mean". In: NIST/SEMATECH e-Handbook of Statistical Methods, Retrieved:2021-09-19.
  • QUOTE: Confidence limits for the mean (Snedecor and Cochran, 1989) are an interval estimate for the mean. Interval estimates are often desirable because the estimate of the mean varies from sample to sample. Instead of a single estimate for the mean, a confidence interval generates a lower and upper limit for the mean. The interval estimate gives an indication of how much uncertainty there is in our estimate of the true mean. The narrower the interval, the more precise is our estimate.

2021b

• (ReliaWiki, 2021) ⇒ http://reliawiki.org/index.php/Confidence_Bounds, Retrieved:2021-09-19.
  • QUOTE: Confidence bounds are generally described as being one-sided or two-sided.
    

Two-Sided Bounds: When we use two-sided confidence bounds (or intervals), we are looking at a closed interval where a certain percentage of the population is likely to lie. That is, we determine the values, or bounds, between which lies a specified percentage of the population. For example, when dealing with 90% two-sided confidence bounds of $(X,Y)$, we are saying that 90% of the population lies between $X$ and $Y$ with 5% less than $X$ and 5% greater than $Y$.

2020

• (DeCook, 2020) ⇒ Rhonda DeCook (2020) "Chapter 8: Statistical Intervals for a Single Sample", Retrieved:2021-09-19.
  • QUOTE: Section 8.2: CI for $\mu$ when $\sigma^2$ unknown & drawing from normal distribution:
    • We use the observed $\overline{x}$ as the point estimate for $\mu$.
    • We provide a two-sided CI for $\mu$ as a ‘window’ or interval for which we are fairly confident the unknown population mean $\mu$ lies.
    • $\overline{x}$ will be at the center of our two-sided CIs:
      $[\overline{x} − cushion, \overline{x} + cushion]$

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