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Quants: confidence interval vs z value vs chebyshev’s

  • This topic has 3 replies, 3 voices, and was last updated Apr-17 by Lagarta.
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    • aanchalb
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      So i am revising quants, and i cant understand the difference between
      i)Chebyshev’s inequality
      ii)Confidence Interval
      iii)Z-value
      iv)t-value

      They all seem the same to me!

    • Snippy
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      Yeah, this happened to me earlier, confused the hell out of me. Not anymore though.

      Okay first, Chebyshev’s inequality. It says that for any sample or population distribution, the % of observations that lie within k standard deviations of the mean is at leat 1 – 1/k^2 for every k greater than 1.

      Second, confidence interval. It is a range of values that we expect the random variable to be in, for a certain percentage of time. It is also 1 – significance level and hence it can be stated as the probability of failing to reject a hypotheses when it is true or as 1 – Type 1 error.

      Third, z-value (z-statistic) is used when the distribution is normal with a known variance whether the sample is small or large, i.e., lesser than 30 or greater than and equal to 30.

      Fourth, t-value (t-statistic) is used when the distribution is normal with unknown variance for small and large samples and also when distribution is non-normal.

      I hope this is what you were looking for.

    • aanchalb
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      Yea. thanx.
      this really helps.

      One thing though, how would we calculate z or t values? Will we hav tables? Or can we rely on not being tested on such calculations?

    • Lagarta
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      @aanchalb I am pretty sure they will provide the necessary tables if calculations are required. HOWEVER, you should know that the Z critical value for your confidence intervals: Z (1 stdev, or alpha=.1 AKA 90% confidence) ~ 1.645, Z (2 stdev, or alpha- .05 AKA 95% confidence) ~ 1.96, Z (3 stdev, or alpha=.01 AKA 99% confidence) ~ 2.58. These are easy test questions, and you should know them well.

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