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Consider a random variable X ~ N(μ, σ), where both μ and σ are unknown. Suppose we have n 1.1.0. samples generated from X. How do we construct a 95% confidence interval? Consider the cases n-: 10 and 1000. Use simulation to validate this confidence interval.

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Given that x~N(u,6), where mean=ur and variance both are unknown P arameters Suppose x , X2 xn are n İ.id samples generated from x him ro con s truet, g5%C-1. for | Aim: To construct g5% CI for et us consider Then test stutisties is given as when σ is unknown variance C6) when u is unknown τhen test statistic s issíven a s follow, x-uon t distribution with n-i) degree of freedom distribution with 100(1-4)7. CI for population mean(u) with population varian ce ( unknown that, i。。(1.4) know c·エ· given as . we where d=5% level d 2 n-lt where Variance (a) is own we get 95 C.1 or vayianie(a) we reuplace d by S such that 2. We get a s g5%C-1 for mean (U) Let n=10

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