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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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Calculate prediction interval

I am trying to use the formula $\tilde{x}^n_{n+m}\pm c_{\alpha/2}\sqrt{P^n_{n+m}}$ to calculate a prediction interval, $\tilde{x}^{100}_{101}\pm c_{\alpha/2}\sqrt{P^{100}_{101}}$ where $\tilde{x}^{100}...
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confidence intervals with normalized data

I am trying to create confidence intervals with normalized data in matlab and am struggling. Since my data is normalized I can't have data that falls below 0 or above 100, however my calculated ...
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Construct an approximate 0.95 confidence interval for alpha (Pareto distribution)

I tried doing it by using the hint from the final answer but my answer is not the same. I also tried to do it using the mean and variance of Pareto distribution but I also did not get the right answer....
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Using Hotelling's T-statistic to find an elliptic confidence set

The problem: We have samples of sizes ${n_1} = 25,{n_2} = 15,{n_3} = 30$ drawn independently from $N\left( {{\mu _i},{\sigma ^2}} \right),i = 1,2,3$ (normal distributions with same variance). We have $...
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Finding a confidence level given a confidence interval [duplicate]

question is here Let X be a single observation form the uniform distribution: f(x) is a piece wise function where f(x)= $\frac{1}{\theta}$ if $0<x<\theta$ and $0$ otherwise. Suppose we use (X,...
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How to find a confidence interval for difference in response rates?

I found this question on a past exam: I know how to find a confidence interval with one mean: $\bar x \pm z_{\alpha/2} \frac{\sigma}{\sqrt n}$ and I also know how to do it with two means however ...
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34 views

Finding confidence level

I am studying for my upcoming stats final exam and I come across this question: Let X be a single observation from the uniform distribution: $$f(x) = \begin{cases} 0 & \text{otherwise} \\ ...
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Chi-squared confidence intervals for big measurements

Let's say I have some observational data. For example: in a certain wavelength interval I measure the flux, 10 000 points, and I have the uncertainty for each one of them. For example: ...
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confidence interval calculation and z score

I have these 2 examples: and in step 1 of solution, for the first one we have 1-0.9 but for the second one we just have 0.95 Why this happened?
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“Weak” conditions necessary for convergence of parameter being in bootstrap pivotal confidence interval?

My statistics text says that: In summary the $1-\alpha$ bootstrap pivotal confidence interval is: $$C_n = (2\hat{\theta}_n - \theta_{1-\frac{\alpha}{2}}^{*}, > 2\hat{\theta}_n - \theta_{\...
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What statistical test solution should I use?

I tested an older software and I found one fault per 10 hours run/10 times run. New version of the software has created. How can I prove the software is operating correctly. How many test should I run?...
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Monthly profits - two tailed tests & finding whether one company's monthly profit is larger than the other's

I have a question below revolving around two tailed tests, confidence intervals, etc, and I'm really struggling to figure out how to find the correct answers. It's 3am and this is the last question ...
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Statistics Confidence Intervals - Don't Understand Solutions

So I have solutions to two statistics questions below, but I don't quite understand where some values came from and was hoping someone could clarify. I bolded the steps I didn't understand and also ...
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Statistics - constructing and interpreting confidence intervals

I attempted to solve the following statistics questions below and I was wondering if someone would be willing to check my answers and confirm they're correct? I was also wondering if there is a way I ...
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1answer
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Exact Confidence Interval for Uniform Parameter

I am given the following. $$X_1, X_2,...,X_n \sim U(0,\theta)$$ and I want to get an exact confidence interval of $\theta$ without using normal approximation. What I know so far is that $Y_n=max(x_1,...
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The Exact Confidence Interval for an MLE of a Gamma Distribution

Above here is the information I've been given for one of my seminar questions, so far I have calculated the fisher information and from there I computed the asymptotic distribution for $\hat{\lambda}$ ...
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How to find confidence interval of bias of unfair coin?

Suppose I have a coin and I suspect it is unfair. I've flipped it ten times and gotten heads without fail. As this question explains, the most likely bias* of the coin is 1. That is, it will always ...
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How to calculate confidence interval

Say you have two versions (implementation) of some logic - V1 and V2. You have to find out if both the logics are consistently producing same results. For example, I have got data 'a'. When run ...
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1answer
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90% Confidence Interval

A random sample of $504$ out of $1600$ students in a school play soccer. How large should the sample of students be if a $90$% confidence interval is desired with a margin of error of $2.2$ percentage ...
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Hypothesis test concerning a population proportion

The problem states that the national on-time arrival rate for flights in Nov 2018 is 79.66% according to the Bureau of Transportation. Suppose in Nov 2018, we ...
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1answer
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Normal approximation of MLE of Poisson distribution and confidence interval

Let $(X_1,\ldots,X_n)$ denote a random sample from a Poisson distribution with parameter $\lambda$. Maximum Likelihood Estimate of $\lambda$ is given by $\hat{\lambda} = \bar{X} = \frac{1}{n} \sum\...
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Confidence Interval - Misunderstandings

Possible misunderstandings of the confidence interval definition keep on bugging me from time to time, and I want to get this sorted. More specifically, I refer to a misunderstanding I believe well ...
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Estimated change in population and confidence interval

In a survey of 500 people selected at random, 345 people are asked if they love to travel alone. (a) What is the estimated proportion of the population that love to travel alone? $$\hat{p}=\dfrac{X}{...
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Proportion Confidence Interval [duplicate]

I understand this: There is a 95% chance any sample from a binomial distribution of samples of size n will have a sample proportion of success between: $$p\pm 1.96*\sqrt{\frac{p(1-p)}{n}}$$ I don't ...
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Interpretation of confidence intervals

I’m studying for an exam and came across a multiple choice question that asked: Which of the following about confidence intervals is true? Apparently, the answer is: For a two sided test, with $...
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Confidence that a statement is false

As a software developer, I have made a program that uploads files one by one to a blob storage in the cloud. After the upload is supposedly complete, a different method will try to verify that the ...
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1answer
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Confidence interval of Pearson’s correlation seems too tight for low N

Say we have a matrix M where each column is a book, each row is a user, and cells are ratings - cells may be empty (not rated), or have values from 1 (didn’t like the book) to 5 (loved the book). If ...
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What is the value of mean so that the probability of random sample mean falling in the observed confidence interval is 95%?

Question: The expression we drive for the 95% confidence interval involves Sn=1/n* sum Xi, i=1 to n, which is a random variable. So, the "location" of the confidence interval is a random variable and ...
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Is Confidence Interval taken on one Random Sample or A Sampling Distribution

I am stuck at CI. Intuitively, a confidence interval (CI) is a type of interval estimate, computed from the statistics of the observed data ( random samples), that might contain the true value (mean) ...
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Confidence intervall for Rayleigh distribution's parameter?

I manage to estimate $\sigma$ in the Rayleigh distribution, but how do I get a correct confidence interval for it? The Rayleigh distribution is $$f_X(x)=\frac{x}{\sigma^2}e^{-\frac{x^2}{2\sigma^2}}.$...
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Confidence intervals & estimation of standard error

Qn: 'You want to estimate the mean number of sentences in a magazine advertisement. How many magazine advertisements must be included in the sample if you want to be 95% confident that the sample mean ...
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what's the consequence/meaning of using estimate for mean/std when calculating confidence interval?

I understand https://math.stackexchange.com/a/192910/291153 and I could rephrase it something like : ...
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Understanding the lower and upper limit of a graph

I was recently presented the following graph: I was given very little context and I have to recreate it. I don't want it to be done for me, but some context would help. Any idea what these upper and ...
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1answer
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Confidence interval for mean of non-normal distribution based on a small sample

The following problem appears in chapter 7 of Probability and Statistics for Engineers and Scientists by Ross: Suppose that a random sample of nine recently sold houses in a certain city resulted ...
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1answer
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How to compute asymptotic confidence interval for linear regression?

Just to make it simple, let us assume we have data $(x_1,y_1), (x_2, y_2),...,(x_n,y_n)$ and perform a linear regression: $y = \alpha + \beta x + \epsilon$ I know how to compute the exact confidence ...
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Going from confidence intervals to likeliness

Long time listener, first time caller. I have searched and searched and can't find an answer to this. It's not from a textbook, it's a part of a project of mine, so if you can help I appreciate it! ...
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Calculate the confidence interval of parameter of exponential distribution with summarySE in R?

I am trying to calculate the confidence interval for a set of data with the assumption they follow Exp dist. To achieve this, I am merging this with this in R, but does not work as I am not very ...
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Finding confidence level given confidence interval and sample size

Question: The Austin-American Statesman asked an SRS of 100 Austinites for their opinion about Mayor Adler's performance. Using the results of the sample, the C% confidence interval for the ...
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Why does $\sqrt{n} (\bar X - \mu)/S$ have approximately a $t$-distribution?

Suppose that the random variables $X_1,\ldots, X_n$ are independent and identically distributed with mean $\mu$ and variance $\sigma^2$. Let $\bar X = (X_1 + \cdots + X_n)/n$ be the sample mean and $S ...
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How to calculate Measurement error of n measurements based on standard error and the quantile funcion

Let's say I have $n$ measurements $x$ sampled from a normal distribution X and I would like to estimate the mean with errors. Is the belove method correct? I'm mostly concerned about if I'm wording ...
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1answer
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Changing the null hypothesis in a t-test

Hello. I am working on a problem and am confused. What I know so far is that the two-sided t-test with $\alpha=.05$ will reject the null since the $p-$value is smaller. Here is where I am lost. The ...
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1answer
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Calculating a 95% confidence interval for the difference of two random variables

Let $ x_1, ..., x_9 $ and $ y_1, ..., y_8 $ be two random samples of two populations. $ \bar x = 7 $ is the mean of the first and $ \bar y = 11 $ the mean of the second sample. The sample standard ...
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Confidence intervals under a function

Suppose we have a 95% confidence interval for a parameter $\theta$. Say that the lower and upper bounds are $\theta1$ and $\theta2$ respectively. Given a continuous , strictly increasing function f, ...
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confidence interval with MLE estimator

$f_{\theta}(x) = 2 \theta x e^{- \theta x^2} $ on the interval $(0, \infty)$. T is the MLE estimator of $\theta$. We construct the confidence interval of $\theta$ $(aT, bT)$, where $a$ and $b$ are ...
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Confidence interval for $ \beta $ given only $\hat{\alpha}$ and $\hat{\beta}$ in linear regression

Assuming that there is a correlation between the random variables X and Y, the line of regression was estimated based on 30 values $ (x_{i}, y_{i}) $(where 200 $\leq$ x $\leq$ 250 ) $: $$ \hat{y} = ...
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How do I pick a rule for decision of a bilateral test?

I have a two random samples normally distribution of length $m = 10$ and $n = 12$. Everything independent. I need to find a rule of decision of level 95% for the hypothesis of equality of the two ...
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Let $X_1…X_9 \sim X$, with X exponential of parameter $\lambda$

Let $X_1...X_9 \sim X$, with X exponential of parameter $\lambda$ all independent. Suppose we know that $\sum_{j=1}^0 X_j = 9.15$ I want to find a confidence interval of level $95$% of $\lambda$. I ...
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1answer
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How should I calculate mean CI - from raw data or mean values?

I have experimenatal data from medical industry. In the experiment 4 observations were weighted, each one 2 times for more precise measurement. As a final weight, a mean from each pair is reported. ...
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Predicting maximum yield using R linear regression output

I have a question in a paper that involves calculating the maximum yield based on a linear model in which yield is explained by the amount of something being transported plus the number of days it is ...
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