Suppose you take 3 samples and report a 99% confidence interval for each dataset. How would you go about calculating the probability that all the datasets contain the true population mean? No other statistics are provided.
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Well what you could say is that if you repeated this experiment of generating three 99% confiodence intervals independently many times, the percentage of the time that the three intervals will all include the true mean is $100\times .99^3$ which is what Stephane said and is I think what the author intended. |
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I'll be careful with this question and suggest you to be careful with the answers. Recall that a $100\alpha\%$ confidence interval DOES NOT MEAN that there is a probability $\alpha$ of finding the true mean in the interval: remember that the true mean, $\mu$, is in the interval or it is not. This mean is not a random variable and, therefore, we cannot associate probabilities to it: the statistic, on the other hand, is random. With that stated, I don't know if your question really makes sense. For more information about what confidence intervals really are, please read this post! |
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