# Questions tagged [confidence-interval]

In statistics, a confidence interval (CI) is a type of interval estimate (of a population parameter) that is computed from the observed data.

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### A little help with confidence interval estimation (for poker database analysis)

I'm a poker player, and I do a lot of database study to understand the frequencies of different profiles of players, to figure out how often they're bluffing and folding in different situations. I'll ...
1 vote
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### Inequality between length of confidence intervals

For given statistical model $(\mathcal{X},\mathcal{B},\mathcal{P})$, where $\mathcal{P}=\{B(1,\theta)^{\otimes n}:\theta\in (0,1)=\Theta \}$, $B(1,\theta)$ is a Bernoulli-trial with success ...
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### What is the (fully rigorous) definition of a confidence interval?

In a nutshell: what is the (fully rigorous) definition of a confidence interval? In page $92$ of Wasserman's All of Statistics, it is written that A $1 − α$ confidence interval for a parameter $θ$ ...
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### Confidence interval for difference between means

I have the following information about data: $$\sum_{i=1}^{12}x_i=2114; \;\sum_{i=1}^{12}y_i=2144;\;\sum_{i=1}^{12}x_i^2=373160;\;\sum_{i=1}^{12}y_i^2=383666$$ And I want to calculate the confidence ...
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### Confidence interval for parameter of normal distribution $X_i\sim N(\theta,\theta^2)$ with equal mean and standard deviation

A sample $X_1,\dots,X_n$ is drawn from the normal distribution $N(\theta,\theta^2)$. I am asked to find a $90\%$ confidence interval for the population mean $\theta$. Let $X_i\sim N(\theta,\theta^2)$ ...
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### Poisson distribution coverage probability for confidence interval.

I have been trying to solve this problem 9.24 of Statitical inference by Casella and Berger. I was able to understand in the theory that confidence interval for Poisson distribution is based on chi-...
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### RMS/quadratic mean and confidence interval

After searching on the web without success, I'm asking for help here. I wasn't taught statistics, and I get lost in a lot of formulas that I often find hard to understand. I'm also not used to posting ...
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### Confidence interval 100 coin tosses, 52 heads?

I am really confused about the confidence interval for n=100 tosses and k=52 heads. If I estimate the probability $\hat{p}$: $\hat{p} = \frac{52}{100} = 0.52$ $Var(\hat{p}) = pq = 0.52 * 0.48 = 0.2496$...
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### Definition of confidence interval - intuition

In the context of the confidence interval for parameter $\theta$ with confidence level $1-\alpha$ I was always dealing with such formulation, $P(\theta \in \mathbb{T}_n)=1-\alpha$, with the "=&...
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### Two sample test - distribution of pooled variance estimator

I am attending a statistics course this semester and although it is offered by the math department the precise assumptions underlying the main theorems are not provided, let alone the proofs. That ...
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### Use prediction interval to get possible values for x given y?

I have the linear model $y = \beta x + \alpha + \epsilon$ with $\epsilon$ i.i.d normally distributed with variance $\sigma^2$. I fit the linear regression using OLS and compute a prediction interval ...
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### How do i make prediction intervals without normally distributed residuals?

I have made predictions for the amount of conversions of a particular website. After predicting the amount for every day. I looked for ways to get a prediction interval for every day. The residuals ...
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### Prediction interval for AR(1) forecast

This link (and others, e.g. slides 43 and 46 of this) say that: Where all the coefficients in the model are point estimates, we could calculate the MSE to generate distributions for the distribution ...
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### Please help me derive the formula for upper bound for one sided confidence interval $\bar{x} + z_{\alpha}(\frac{\sigma}{\sqrt{n}})$?

I want to derive for myself the known formula for the upper bound for one sided confidence interval $\bar{x} + z_{\alpha}(\frac{\sigma}{\sqrt{n}})$ for mean $\mu$ for a sample of size $n$ from a ...
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### Accounting for an uncertainty in the number of categories of the multinomial distribution

Assume that we have an unfair die, and our task is to determine the probabilities of rolling a 1, a 2, a 3 and so on by rolling the die. Unfortunately we have no way of knowing how many sides the die ...
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### Determine if a $95\%$ confidence interval for $\theta$ is equal to a given set

So I need to decide if the following statement is true or false: Let $X_1,X_2,...,X_n \sim N(\theta,1)$. Then a $95\%$ confidence interval for $\theta$ is all of the values of $\theta$ that satisfies: ...
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