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.
0
votes
0answers
19 views
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}}.$...
0
votes
0answers
8 views
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 ...
0
votes
0answers
7 views
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 ...
1
vote
0answers
49 views
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 :
...
0
votes
1answer
17 views
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 ...
2
votes
1answer
27 views
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 ...
1
vote
1answer
18 views
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 ...
0
votes
0answers
10 views
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!
...
1
vote
0answers
27 views
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 ...
0
votes
1answer
28 views
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 ...
-1
votes
0answers
14 views
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 ...
0
votes
0answers
28 views
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 ...
0
votes
0answers
14 views
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 ...
0
votes
1answer
19 views
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 ...
0
votes
1answer
26 views
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 ...
0
votes
0answers
11 views
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, ...
1
vote
1answer
15 views
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 ...
0
votes
0answers
15 views
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} = ...
0
votes
0answers
6 views
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 ...
0
votes
0answers
16 views
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 ...
2
votes
1answer
21 views
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. ...
0
votes
0answers
39 views
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 ...
0
votes
0answers
8 views
0
votes
0answers
21 views
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 ...
0
votes
0answers
15 views
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. ...
0
votes
0answers
17 views
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, ...
1
vote
0answers
29 views
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 ...
0
votes
0answers
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 ...
0
votes
1answer
26 views
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 ...
0
votes
0answers
17 views
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 ...
0
votes
0answers
13 views
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) ...
0
votes
0answers
19 views
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....
1
vote
1answer
109 views
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{\...
0
votes
0answers
34 views
$X_1$,$X_2$…$X_n$ 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.
0
votes
0answers
13 views
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 ...
1
vote
0answers
32 views
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% ...
0
votes
1answer
17 views
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.
...
0
votes
0answers
13 views
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 ...
0
votes
0answers
16 views
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 ...
2
votes
0answers
27 views
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 ...
0
votes
0answers
26 views
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 ...
0
votes
0answers
22 views
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 ...
0
votes
0answers
28 views
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 ...
1
vote
2answers
14 views
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 ...
0
votes
2answers
14 views
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 ...
0
votes
1answer
13 views
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?
...
1
vote
0answers
14 views
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 ...
0
votes
1answer
14 views
find a 99% confidence interval given ∑<sub>i=1</sub><sup>61</sup> X_i = 6450 and ∑<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 ...
0
votes
1answer
55 views
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 ...
1
vote
1answer
42 views
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)....
