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# May I ask how I can get the 95% confidence intervals for the true mean data?

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"A" is data with 700*1 matrix.

I want to have the 95% confidence intervals for the true mean of A.

What codes do I have to use?

Thanks

##### 13 Comments

John D'Errico
on 22 Oct 2022

Edited: John D'Errico
on 22 Oct 2022

How is this a question about MATLAB? Anyway, read here:

William Rose
on 23 Oct 2022

The wording of your question, "...get the 95% confidence intervals for the true mean...", is thought-provoking. A strict interpretation of the p% confidence interval (X1,X2) is :

IF the true mean μ and true variance are what we estimate them to be ( and ), and if the variable has the distribution we think it has (and those are significant ifs), THEN, if we redo the sampling experiment many times, the sample mean, , will be between X1 and X2, p% of the time.

The corrollary, which is simpler to state and understand, is

There is a p% chance that the true mean lies within (X1,X2).

Some quibble a bit with the statement above, because the C.I. (X1,X2), which we estimated from a set of observations, either does (100%) or does not (0%) include the true mean - we just don't know if it does or doesn't. In this view, it is more correct to say

Confidence intervals constructed this way include the true mean p% of the time.

dpb
on 23 Oct 2022

"Confidence intervals constructed this way include the true mean p% of the time."

Again note the implied but left out for brevity is that the above is specifically true IFF the assumption of normality is also true.

BUT, the sample mean is also a statistic and by central limit theorem, a random sample of the means of estimates of the mean of any distribution will approach normality so the above is still liable to be ok even for at least moderately skewed distributions. But, if sample sizes are small (<=30 is a commonly used size), one should use the sample-size correction of substituting the t-distribution limits for normal z-points.

A page I just happened across does a pretty nice job here...<confidence_interval_of_a_mean_normal_approximation_method-principles-properties-assumptions>

the cyclist
on 23 Oct 2022

Edited: the cyclist
on 23 Oct 2022

All of the above also assumes that the vector of 700 is a sample of a population, and we are trying to estimate the population mean.

:-)

I'll see myself out.

William Rose
on 23 Oct 2022

@dpb,

"I thought of going there, too, but for once was less wordy... :)"

Ha ha! I know you and @John D'Errico know all that CI stuff better than me - I just couldn't resist, I guess.

@Chris, you're welcome.

dpb
on 23 Oct 2022

John D'Errico
on 23 Oct 2022

At the very least, ask questions about statistics on a statistics forum.

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