# 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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### Confidence interval of a random variable

Given $Θ$ is an unknown, and $X$~$U(Θ-0.5,Θ+0.5)$ Is $[X-2,X+2]$ an 80% interval? Apparently, yes it is: $$P(X-2≤Θ≤X+2)=P(Θ-2≤X≤Θ+2)=1$$ The transition from $P(X-2≤Θ≤X+2)$ to $P(Θ-2≤X≤Θ+2)$ is ...
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### Difference between mean response at $x_0$, and predicted value at $x_0$

I've read a few accounts on the difference between these two, but none have been very clear. So what exactly is the difference between 'mean response at $x_0$' and 'predicted value at $x_0$'? Also, ...
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### Confidence interval for a probability

I'm currently studying the following problem in my textbook: Consider the confidence interval for an unknown probability $p$. Suppose that we want confidence level $0.95$ and that we want the length ...
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### Central Limit Theorem with Confident Interval

Below is a question with two parts- a) and b) and further below the answers. I understand part a). However, part b) has me confused. I understand basic confidence intervals but this seems to be going ...
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### How do I derive a formula for the prediction intervals for the sum of responses of two independent future observations? [closed]

So far I've tried using the formula for confidence intervals for a full rank model and trying to use that to get a prediction interval formula. What I don't understand is how to get a prediction ...
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### Limits vs Confidence Interval, the difference?

Below is a question on "limits" and confidence interval. The answers are below. Why does question b) not require dividing by the square root of 10, but the confidence interval in question c) ...
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### Central Limit Theorem "find sample size" question, with modulus inequality

I'm doing the below Central Limit Theorem question. I omitted sub-question a) and b) as they were unrelated. I have included the answer below the question. I half-understand the answer but I don't ...
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### Why don't n-1 for df in this scenario

Simple statistics question, but can't figured out. What is the critical value t* for constructing a 99%, percent confidence interval for a mean with 11 degrees of freedom? My answer for this is 3....
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### How to derive the formulae for Poisson confidence intervals?

I have been struggling to derive the formulae for CI of Poisson distribution parameters. Suppose I have a sample $X=(X_1,\dots,X_n)\in\text{Poisson}(\lambda)$. Parameter $\lambda=\theta$ is what I ...
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### Determining the sample size to satisfy two tests

A survey of a university's students is to be carried out to estimate both the proportion, $P$, who own a bicycle and the average weekly spend on junk food, $\bar X$. It is desired to estimate $P$ with ...
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### Calculate the confidence interval of the parameter representing a logical level

Basically, I have a big dataset including 150+k rows. It consists of completed flights by "N" air company. Each row in the Excel file represents each flight on a special date. The row ...
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### Is choosing confidence interval bounds after observing data mathematically valid?

Let $D$ be a continuous distribution on the interval $[0,1]$ that is not known to us. We have no prior knowledge about $D$. For a given error tolerance $\delta$ we want to find bounds $a, b$ s.t. $b-a$...
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### Confidence bound for a family of lines

I have a family of lines $y_i= a_ix+b_i$ where the pairs $(a_i,b_i)$ are generated by a random process. I can fix $x$ and generate a family of points $y_i$ for which I can estimate the mean and the ...
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1 vote
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### Confidence Interval with the mean being the average of probabilities

Let's say that, in a video-game, every time you go to the blacksmith and there is a random (yet announced) chance he succeeds fixing your weapon. In this example it goes like this: 70% chance ...
1 vote
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### Finding a confidence interval for a binomial proportion without knowing the mean or variance?

I'm just learning statistics and I've been given an interesting problem to solve that I'm unsure how to approach. I've dealt with various tests (t-test, chisq test, confidence intervals etc.) but I'm ...
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I heard that, for example, the number of meteorites that hit the Earth follows the Poisson distribution. My question is how to estimate the Poisson parameter $\lambda$ and confidence interval for this ...