Quants: confidence interval vs z value vs chebyshev’s

@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.

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.