# 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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### Determining precise value using imprecise measurements.

Suppose an accurate scale reports weight rounded to the nearest unit. If it reports the weight of an object as "6", all I know is that it could actually weigh anywhere between 5.5 and 6.5. But I need ...
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### Do you know an interesting problem regarding confidence intervals?

I'm currently studying statistics and I was wondering if any of you have a good and interesting problem regarding confidence intervals (statistics) and its solution that you'd like to share with me. ...
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### Determine the probability that any person is against government decisions

In one study, out of $80$ respondents, $23$ were against going to a concert. Determine if a person is against decisions to go to the concert if the confidence interval is 95%. Help me please. Thanks ...
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### What sample size is needed to ensure a majority?

The results of a sample of voters showed that $55\%$ voted for a given candidate. It was determined that at a confidence level of $0.95$ that candidate would be the winner (i.e. would receive the ...
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### Confidence Interval based on limiting distribution of the Maximum Likelihood Estimator Sigma and Sample Variance

Another statistics question I need some help with. Now, I am not too familiar with limiting distributions (had my course on it over a year ago). I have tried some things myself and ran some ...
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### Show that the Value-at-Risk (VaR) at confidence level $c = 95\%$ is $\text{VaR} = 1$. [closed]

Suppose an asset has return $K = 1$ with probability $\frac{1}{2}$ and $K = −1$ with probabilty $\frac{1}{2}$. Show that the Value-at-Risk (VaR) at confidence level $c = 95\%$ is $\text{VaR} = 1$.
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### Minimum length of confidence interval for $\theta$ when $X_1,\ldots,X_n\sim\operatorname{Beta}( \theta,1)$

I am asked to find the minimum length confidence interval for a Beta distribution with parameters $a=\theta$ and $b=1$ and probability $1-\alpha$. I have found that $-2\theta \sum_i \log(X_i)$ has ...
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### Determining whether to apply unequal or equal variance case for finding the confidence interval for difference between two means

The following data represents the total time taken, in days, to deliver books ordered through two online sellers. The sample delivery times are collected and reveal the following information: Find ...
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### Confidence interval for categorical data

I have the following data: ND NI SC PI PA Green 27 3 9 4 7 Blue 24 14 14 6 8 I want to do the following: Write the multinomial model ...
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### Calculating the margin of error for a one-sample confidence interval for proportions

I recently saw a question that gave a 95% confidence interval for one-sample t-interval for means as (5.6, 7) and was asked to find the point estimate and the margin of error. The solution said that ...
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### To estimate mean of two populations.

Suppose that you are given with two set of sample $F = \{ x_1, x_2,\ldots,x_n\}$ and $M=\{y_1, y_2,\ldots, y_m\}$ ($n=100,$ $m=100$) $x_i$ (or $y_i$) represents the height of a female (or male) ...
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### Sample size in Confidence Intervals

In repeating confidence interval experiments, are we allowed to take samples of different size every time? Because a confidence interval of 95% means that if the sampling process is repeated infinite ...
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### Function of a confidence interval

If we have a confidence interval for a given parameter $\theta$ given as $[\theta_l, \theta_u]$ ($l$ is for lower and $u$ is for upper) at confidence level $\gamma$, and we have a monotone (Borel) ...
### How come we can use the $Z$ table (or $t$ table) when finding confidence intervals?
I am currently learning about confidence intervals and the following question keeps bugging me. How come that when we find a confidence interval I can just use the $Z$ or $t$ table? Let's say that I ...