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Understanding 95% CI for the Mean

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  • #53757

    John Moore
    Participant

    What exactly does 1.4518 < mean <1.4526 mean to me? 95% CI for the Mean:
    1.4518 < mean <1.4526

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    #191342

    Robert Butler
    Participant

    As posted, not much of anything.

    It could be an indication of the standard error of the mean in which case it is telling you that if you were to go out and take another series of independent sample of the process from whence the samples used for calculating the mean (same number of samples in both cases) came then, assuming no significant changes in the process, there is a 95% chance that the new sample mean will fall somewhere inside the confidence interval.

    If the confidence interval refers not to the standard error of the mean but just to the standard deviation of the population used to compute the mean value then the 95% confidence interval would be an estimate of the likelyhood of the range of values for the next independent single sample.

    It could also be an estimate of an adjustment to the estimate of the standard error of the mean where the confidence interval describes the region where one would expect to find sample averages of subgroups of a given size of independent measures.

    Therefore, before you can say much about the meaning of the confidence interval you need to know the basis of the confidence interval.

    – is it the standard error of the mean?

    -is it the population standard deviation?

    or

    is the confidence interval a function of some subgroup sample size?

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    #193705

    Prabhu V
    Participant

    Hi,

    The formula the confidence interval is : P+/- Z alpha/2 * SQRT ((P *(1-P)/n)
    Where P is Population proportion
    n is sample size.

    From the above formula, it is clear that CI is function of Std deviation (Z alpha) and as well as the subgroup sample size.

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    #193707

    Joel Smith
    Participant

    @John-Moore Likely what you are sharing is simply a confidence interval on the mean, probably from a 1-Sample t-test. What this means is that based on your sample, there is a 95% chance that the true mean is between 1.4518 and 1.4526 (assuming your sample was randomly taken from a stable process).

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    #193713

    Robert Butler
    Participant

    I realize that the term “95% CI for the Mean” SHOULD mean what the previous two posters have suggested it means but I’ve seen far too many instances where, once the appropriate information had been supplied, that phrase was applied to other circumstances such as those enumerated in my initial post. As I noted initially, I would not offer a “translation” without additional information.

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    #193742

    Ken Feldman
    Participant

    @prabhuvspj Looks like you are a little clueless. You provided a confidence interval “ESTIMATE” for a proportion using an estimate based on the normal distribution. If you are really doing a proportion, you should have used the actual binomial calculations. There are lots of CI for just about anything; means, proportions, variances, y intercepts, process capability, differences in means, slopes and on and on. I agree with Robert that the original poster provided way too little info to be useful.

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