Quick question about means/confidence intervals

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The Racist Dragon
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Report Thread starter 6 years ago
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If I am given the standard deviation, the mean and the number of observations of a random variable, how do I work out the confidence level of the true mean being within 10% of the mean. i.e. the confidence that the true mean = estimated_mean \pm 0.1*estimated_mean

Help would be appreciated.

EDIT: click here for new thread, this one has too much unnecessary info in it.
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CTArsenal
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(Original post by The Racist Dragon)
If I am given the standard deviation, the mean and the number of observations of a random variable, how do I work out the confidence level of the true mean being within 10% of the mean. i.e. the confidence that the true mean = estimated_mean \pm 0.1*estimated_mean

Help would be appreciated.
It depends on the sample size.

A large sample size you can use the normal distribution, a small one and you use the t-distribution.

For instance, for a normal distribution, the confidence interval is:
[\bar{x} \pm Z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt n}]

For a t-distribution, the confidence interval is:
[\bar{x} \pm t_{n-1}(\frac{\alpha}{2}) \times \frac{\sigma}{\sqrt n}]

\alpha being the significance level, i.e. in this case, 0.1.
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The Racist Dragon
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Report Thread starter 6 years ago
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(Original post by CTArsenal)
It depends on the sample size.

A large sample size you can use the normal distribution, a small one and you use the t-distribution.

For instance, for a normal distribution, the confidence interval is:
[\bar{x} \pm Z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt n}]

For a t-distribution, the confidence interval is:
[\bar{x} \pm t_{n-1}(\frac{\alpha}{2}) \times \frac{\sigma}{\sqrt n}]

\alpha being the significance level, i.e. in this case, 0.1.
The confidence level is what I'm calculating, I want to know the confidence level that the true mean is within 10% of the estimated mean, i don't want the 10% confidence interval of the estimated mean.

I know it's a little confusing, I had to read the question a few times myself...!

So far I have calculated that:

Z_\frac{\alpha}{2} = \frac{0.1*mean*\sqrt{n}}{stdev}

But I don't know how to find \alpha from that, I'd probably need some crazy formula...

I think I should make a new thread asking how to find alpha when I already know what Z is, this thread has too much unnecessary info in it.
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