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### What is the fundamental confidence interval fallacy? [duplicate]

Beginner question here. I've read (see this paper) that when computing confidence intervals if you get a given interval with a confidence level of 95%, then it is a fallacy to think that the true ...
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### Working on Confidence Interval and its meaning [duplicate]

Supposed in a population, I take a sample with a size of 1500 to build a 96% confidence interval for the true mean $\mu$. Then such an interval is assumed to range from 6.8 to 8.0. Assume the sample ...
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### Confidence interval interpretation [duplicate]

Why it's said when we estimate a parameter, from 100 confidence intervals, 95 will have the parameter. And why it is incorrect to say that is a 95% probability that the true parameter is in the ...
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### Aren't these statements about confidence intervals equivalent? [duplicate]

I just read the following sentence from Wikipedia: A 95% confidence interval does not mean that for a given realized interval there is a 95% probability that the population parameter lies within ...
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### Does it make sense to speak of probability of a hidden outcome? (context: confidence intervals) [duplicate]

My question is concerning the frequentist approach to probability. Assume that you tossed a coin but don't see the outcome. Does it make sense to say that it shows head with a probability of 0.5? Or ...
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### Confidence Intervals meaning [duplicate]

Lets say I know population std. deviation $\sigma=5$ and sample size $n=60$. Now lets say my sample mean is $\overline{X}=98$. I already know from central limit theorem that 95% of the time the sample ...
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### How are statistics on scientific papers inferred? [duplicate]

Referring to this question: How should be statistics on scientific papers read?, a kind user explained us how to read the following statement from the original research paper:. Increasing ...
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### Why confidence interval is important when point estimator is close to zero? [duplicate]

When the point estimator is relatively small numbers, a confidence interval is likely to contain zero, be fairly wide and include both positive and negative values. Basically, when CI contains zero ...
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### Interpretation of confidence intervals [duplicate]

CI(p) = (a, b) People sometimes interpret this interval by saying that there is a 95% probability that the true p belongs to (a, b) The statement is incorrect (there is no probability associated ...
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### Difference between 95% of confidence intervals containing mean vs 95% probability of one interval containing the mean? [duplicate]

Given a random sample $x$ and wishing to estimate the value of mean $\mu$ of a population from which $x$ was drawn, I construct a 95% confidence interval $CI_{x}$ using $\mu_{x}$ and $\sigma_{x}$. If ...
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### Difference in CI Interpretations? [duplicate]

So the interpretation of a 95% CI is that there is a 95% probability that the CI contains the true parameter value, but not that there is a 95% probability that the true parameter lies in the CI? Can ...
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### Interpretation of a Confidence Interval [duplicate]

If you compute the 95% CI for a population mean from a given sample, apparently it is taboo to say something like "there is a probability of 0.95 that the true mean lies in this specific CI". Yet ...
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### Confidence Level and Interval probability [duplicate]

I understand that the confidence level denotes how reliable is my test and the confidence level is not the probability associated with the confidence interval. This is well explained on Wikipedia:...
In Example 5 here, the authors discuss polling. Voting for candidate 'A' is given the numerical value of 1, and voting for 'B' has the value of 0. The CLT says that the average of a sample of $n$ ...