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

"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

[John D'Errico]

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

https://www.statology.org/confidence-interval-mean/

[Chris]

Thank you so much!

[dpb]

I'll again refer back to <NIST handbook 7.1.4>.

[William Rose]

@Chris,

@John D'Errico and @dpb both give good citaitons.

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.

https://journals.physiology.org/doi/full/10.1152/advan.00006.2009

[dpb]

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

Yes, @William Rose, I thought of going there, too, but for once was less wordy... :)

[Chris]

Thank you so much for telling me!!

[dpb]

"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]

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]

@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.

And that other site you found is good.

@Chris, you're welcome.

[dpb]

It's probably time for @Chris to find the uni stastical consulting guru or his advisor and get more informed advice on his real problem. The basic rules are possible to be given, but to really know about applying to a specific problem one needs to know what the problem actually is.

[Chris]

I really appreciate your help and explanation. Thanks a lot.

[John D'Errico]

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

[Adam Danz]

@Chris here's my wordy response to a similar questions 3 years and 2 days ago.

https://www.mathworks.com/matlabcentral/answers/487518-bootstrap-confidence-interval-90#answer_398347