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.
791
questions
2
votes
0
answers
49
views
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 ...
- 21
1
vote
1
answer
47
views
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 ...
12
votes
5
answers
1k
views
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 $θ$ ...
- 5,166
0
votes
0
answers
11
views
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 ...
- 893
0
votes
0
answers
17
views
Finding α-Quantiles of χ2 Distribution for Variance Estimation
I posted this same question yesterday but it got closed because i hadn't met the guidlines for questions, my apologies guys, so i'm going to re-write it better this time.
Exercise 17. Let $X_1, \ldots,...
- 17
0
votes
0
answers
7
views
Confidence Interval for Regression Values
From this article, I understand the idea behind the Confidence Interval for the Individual Response.
However I don't understand the part on ...
- 15
0
votes
0
answers
15
views
Calculating confidence interval while fitting multiple datasets simultaneously.
I am dealing with six experimental datasets of two species interaction and I want to fit these six datasets to a coupled ode system simultaneously to get a set of estimated parameters and ...
- 330
0
votes
1
answer
132
views
Likelihood ratio test of Poisson distribution
I'm given this problem:
Let $X_1,...X_{100}$ be a random sample from a Poisson distribution with mean $\lambda$. Consider testing the hypothesis $H_0$: $\lambda=1$ vs $H_1$: $\lambda<1$. Consider ...
- 1
0
votes
1
answer
25
views
Confidence Interval for Expected Value of Binomial Distribution
been trying to wrap my head around this for a while. What is the confidence interval for the expected value for a binomial distribution?
Let's say for a sample, I throw a coin 7 times and only 1 is ...
- 15
1
vote
1
answer
15
views
Missing N in confidence interval for binomial distribution
I am studying on confidence interval for binomial distribution recently. I know general formula for confidence interval is $$ z1⋅\frac{σ}{\sqrt{n}} $$
if I substitute the formula for variance for ...
- 15
0
votes
0
answers
17
views
Confidence Interval of Continuous Statistic Model
Let $(\mathcal{X}\subseteq \mathbb{R}^d, \mathcal{F}=\mathcal{B}(\mathbb{R}^d)\vert_{\mathcal{X}},\{P_{\vartheta}|\vartheta \in \Theta\})$ be a continuous statistic model, $\rho:\mathcal{X}\times \...
- 27
6
votes
2
answers
213
views
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 $X_i\sim N(\theta,\theta^2)$ ...
- 657
0
votes
0
answers
14
views
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-...
- 11
0
votes
0
answers
26
views
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 ...
- 1
0
votes
0
answers
37
views
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 $\hat{p}$:
$\hat{p} = \frac{52}{100} = 0.52$
$Var(\hat{p}) = pq = 0.52 * 0.48 = 0.2496$...
