What is the rule of 1.96 for estimating confidence intervals?

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Gideon Hutchinson · Accepted Answer

Step 1The value of 1.96 stems from the fact that we generally use 5% significance level in computing the confidence interval or any hypothesis testing.When we are looking for a two sided confidence interval of mean, we want to find the a value less than the sample mean, let it be LL and another value above the sample mean, let&#039;s call it UL. Now these values are chosen in a manner that when sampled large number of times, the true mean will lie between these values 95% of the time.Mathematically, P(LL≤μ≤UL)=0.95Now suppose sample mean, br{X}=0 and σ=1 (That is sampling from N(0,1)). In this case if we want to estimate the true mean μ, what should our UL and LL be?By using the normal tables, we can see that P(z≤1.96)=0.975 and P(z≤−1.96)=0.025. Thus, P(−1.96≤μ≤1.96)=0.95Similarly, for non standard cases, {P(−1.96≤X―−μσn≤1.96)=0.95}.Or, {P(X―−1.96σn≤μ≤X―+1.96σn)=0.95}.Thus, we write the confidence interval as X―±1.96σn.This value would be different if we need confidence interval at some other significance levels. For instance, for 99% confidence interval we shall use 2.576

What is the rule of 1.96 for estimating

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