# 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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### Interpretation of a confidence interval

The textbook, Introduction to Probability by Anderson, Seppalainen, Valko, reads, on page 151, Another task is to find the confidence interval around $\hat{p}$ that captures the true $p$, with a ...
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### Probability inequality for a statistic with lower bound constraint, where McDiarmid's inequality is used in proof

I'd like to prove a probability inequality involving a statistic and a random variable as in the following statement. My questions are two-fold: Is the following proof using McDiarmid's inequality ...
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### Confidence Interval and Hypothesis Test Disagree?

I created a problem where I am having my students complete a hypothesis test and confidence interval for proportions to highlight the connection between the two. However, in doing the problem I am ...
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### Which is the variance of a variable which is the linear sum of normally distributed random variables?

I have a random variable $x$ which is normally distributed with expceted value $\bar{x}$ and variance $\sigma$: $$x\sim N(\bar{x},\sigma)$$ As you know, i can consider $\bar{x}$ a random variable that,...
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### A random sample of $50$ machines obtained that its average life is $\bar{x}=70$ months with a variance of $s^2=49$. Confidence interval for variance.

I need help with the part b) of this exercise. A random sample of $50$ machines obtained that its average life is $\bar{x}=70$ months with a variance of $s^2=49$. Assume that they are normally ...
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### MLE, a book: Statistical modelling and inference using likelihood

I have a problem with a likelihood interval; Here on the page $74$ in the example $4.1$ they write: IN CASE the link doesn't download Please copy the link and paste it to your web browser. The ...
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### How many observations are required to achieve a particular confidence interval for the mean?

Suppose that the standard deviation of an observation in a given population is known to be $\sigma = 15$. How many observations in a sample is needed to estimate $\overline{x}$ (the mean of the sample)...
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### Confidence Interval - Meaning and Interpretations

Could someone please help me understand what exactly "Confidence" in confidence interval actual means? Does it mean, that, (on average or exactly?), we can say, that (for a 90% confidence ...
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### Using Sample Variance to Estimate Population Variance and Sample Size

I am a freshman to statistics, and recently faced a problem with which I need help clarifying. Suppose there are 130 boxes of similar sizes, each containing a random number of chocolate cookies. 15 ...
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### Estimating a highest probability density (HPD) interval

QUESTION: (I translated it into English so you might find somewhat awkward..) A company wants to get information about the lifespan of certain machines. Let's say that the lifespan of the machines ...
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Let $𝑋_1,…,𝑋_𝑛$ be i.i.d. Bernoulli random variables with some unknown parameter $𝑝∈(0,1)$. Then which of the following is/are valid confidence interval(s) for $𝑝$ with nonasymptotic confidence ...
### How to remove $\theta$ from the exponent? (confidence interval)
I'm solving the following mathematical statistics problem Find a 95% confidence interval for $\theta$ where $X_1,...,X_n\sim Beta(\theta,1)$ I started by finding a function in which $\theta$ isn't a ...