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Results tagged with confidence-interval
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user 362774
A confidence interval is an interval that covers an unknown parameter with $100(1-\alpha)\%$ confidence. Confidence intervals are a frequentist concept. They are often confused with credible intervals which is the Bayesian analog.
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Are these two definitions of a 95% confidence interval equivalent?
A definition that I am aware of is interpreted as follows.
Given a fixed probability parameter $\theta$, if I construct $100$ confidence intervals $\{I_1, \cdots, I_{100}\}$, then it is expected that …
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Meaning of 95% confidence interval [duplicate]
If I take a 95% confidence interval $I_k$, then it means that if I sample 100 confidence intervals $\{I_1, \cdots, I_{100}\}$, then it is expected that 95 of $I_k$'s contain the true parameter. Of cou …
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Interpretation of 95% confidence interval [duplicate]
I have a trouble understanding the concept/interpretation of confidence interval. It is commonly said that if I construct a hundred of 95-percent-confidence-intervals, then it is expected that 95 of t …
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Central Limit Theorem and Confidence Interval
Let $\{X_n\}_n$ be a sequence of i.i.d. RV's, where each $X_n$ is a copy of RV $X: \Omega \rightarrow \mathbb R$. For $n > 0$, I can define $\bar X_n := \frac{1}{n}\sum_{i=1}^n X_i$. Then, central lim …
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