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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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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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How to choose the suitable confidence interval for my data? [on hold]

Let's suppose that I have a set of dataset. My data representsFor every dataset, I compute its regression line: y=slope*x +intercept. I extract different slopes. I ...
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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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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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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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T-Intervals vs. Z-Intervals

In my statistics class, we are learning about distributions and z-intervals and t-intervals and when to use them. I know that you use z-intervals for sample proportions and t-intervals for sample ...
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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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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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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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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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Probability of probability / Confidence in probability

Actually I got a few questions on the same topic... I think they are related in the sense that, how do we infer information about an unknown distribution with limited samples. - There's a coin that ...
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How to account/penalize for low sample size when computing performance?

I am interested in analyzing user performance at a per user level. Users have the opportunity to engage with an app by answering trivia questions and can choose how many questions they want to answer. ...
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Why the confidence interval for proportion does not depend on the population size? [duplicate]

The formula for a 95% confidence interval for proportion is $\hat{p}\pm 1.96 \sqrt{p(1-p)}$ Suposing a sample of 200, calculating a proportion of 1.8%, the confidence interval is 1.67% - 1.93%. But, ...
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Minimum Sample size between two samples for a specified confidence interval/level with sigma known

Hi math stack exchange, I came across the following question and found it quite interesting and am struggling to solve it. I haven't seen anything like it because it is both two sample and has sigma ...
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37 views

Sampling uncertainty (uncertainty in standard deviation)

Say I took twenty measurements of the wind velocity at a point. This is a sample of the infinite number of measurements I would need to get the true velocity at that point. I then calculate the mean ...
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1answer
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Confidence Interval question for amount of experiments one should do.

Before posing this question, the lecture notes I am reading discussed games, probability, the binomial distribution and central limit theorem. It usually assumes some form of game when it asks ...
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convergence of two sample means as a function of sample size and confidence level

I tried to derive an equation for one sample mean to converge to another sample mean within a 95% confidence interval, but I know I am wrong. Can someone tell me what I did wrong, and what is the ...
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Confidence interval for multinomial parameters

I wonder how we can make confidence intervals for the parameters of a multinomial distribution. For example, suppose that we ask in a survey: what's your favourite hot drink: 1) Coffee 2) Thee 3) ...
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Non normality on confidence interval

I've constructed a confidence interval for one mean under the assumption that the distribution follows a normal distribution. I am to comment on the importance of normality for the confidence interval....
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Logistic Regression: Asymptotic confidence interval for the lethal dose

For the logistic model: $$\log \Big( \frac{\pi(x)}{1-\pi(x)}\Big) = b_0 +b_1x$$ I want to construct a asymptotic confidence interval for the ratio of the m.l.e's of $b_0$, $b_1$: $LD50 = -\frac{\...
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$X_1$,$X_2$…$X_n$ are iid N($\mu,\sigma^2$). Derive a confidence interval for the parametric function $\mu+\sigma$ and $\mu/\sigma$.

I know how to find confidence interval for each of the parameters $\mu$ and $\sigma^2$ but don't know how to find in the case of parametric function.
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Sample size and margin of error in a confidence interval for a mean

I am having trouble understanding this problem: Darren wants to estimate the mean age in a population of trees. He'll sample $n$ trees and build a $90\%$ confidence interval for the mean age. He ...
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Reducing the confidence interval with T distribition

My question is the following: The population: weight of apples (in grams). We do not know anything about the population distribution except that it is a normal distribution. We want to find a 90% ...
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Confidence interval…

State whether or not the following is true. Explain why: Someone says that a computed result (0.06,0.07) of a 95% confidence interval of a parameter, β, implies that P[0.06 < β < 0.07] = 0.95. ...
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Maximizing the length of the confidence interval

Let $X_1,X_2,...,X_n$ be iid $Bern(θ)$. (a) Determine the sample size such that the length of 95% confidence interval is at most 0.04. (b) To reduce the cost, assume that the half of the sample is ...
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Confidence intervals and the zeta function?

In my statistics class my teacher introduced us to confidence intervals and handed out a chart of values for the constant/critical value used to determine the margin of error. On the chart, as the ...
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Confidence interval for mean of a normal population

Consider a normal population with unknown mean $\mu$ and variance $\sigma^2=9$. To test $H_{0}:\mu=0$,against $H_{1}:\mu \ne 0$. A random sample of size 100 is taken. Based on this sample, the test ...
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calculating upper limit of confidence interval for normaly distributed sample with sigma unknown

i have following problem, To find the average SAT verbal score in a class, six students are sampled and their scores are 560, 610, 500, 470, 660, and 640. Assuming that students' SAT verbal scores ...
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Constructing an upper confidence limit for $σ^2$

Suppose that $X_1, ..., X_n$ form a random sample from the normal distribution with unknown mean µ and unknown standard deviation σ. Construct an upper confidence limit U(X1, ..., Xn) for $σ^2$ such ...
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Find a 95% confidence interval for the population standard deviation with mean of the population unknown.

A random sample is taken from a random variable W~N(μ, σ). RS: 380, 385, 400, 375, 420, 415, 412, 401, 405, 411, 410, 383. Find a 95% confidence interval for the population standard deviation σ. The ...
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A r.s. of size n is taken from a normal r.v. X~N(μ, 1.5). To be 95% confident that the error between X̄ and μ is at most .85, how large must n be?

Suppose a random sample of size n is taken from a normal random variable X~N(μ, 1.5). To be 95% confident that the error between X̄ and the unknown population mean μ is at most .85, how large of a ...
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Determining $n$ for which the confidence interval will have level of confidence >= 0.9

I have come to the point where there is an $X\text{~}N(a,\frac{9}{n})$ and $\psi$ is its CDF, I have to determine the smallest n for which $\psi(a+1)-\psi(a-1)>=0.9$ I have no idea how to approach ...
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Confidence Interval of number of red marbles among 100 marbles where proportion of red marbles is uniformly distributed

A bag contains 100 marbles of colors red and black. The proportion of red color marbles is uniformly distributed between 0 and 1. How do I compute the confidence interval of the number of red marbles? ...
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Confidence interval of dependant variable individual value by R-squared value

From the physical experiment I've got a sample collection of values (unique Y for each unique X). The problem is to find the ...
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1answer
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find a 99% confidence interval given &sum;<sub>i=1</sub><sup>61</sup> X_i = 6450 and &sum;<sub>i=1</sub><sup>61</sup> X^2_i = 6450

find a 99% confidence interval for the mean given: ∑i=161 X_i = 6450 and ∑i=161 X^2_i = 6450 I found the sample mean of 105.7377 . (6450/61) I do not know how to find the variance. Then ...
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How to calculate sample mean and variance given the confidence interval for the normal?

A random sample of size n=16 is taken from a random variable X~N(mu, sigma), with variance unknown. The 95% confidence interval for mu (44.7, 49.9). What are the values of the sample mean and the ...
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1answer
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Determining sample size given true proportion.

I'm attempting to solve a problem from a statistics course in regards to finding the sample size I need to take when given the Margin of Error, Confidence interval, and 'true proportion' (probability)....