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    Hello all!

    I've been trying to dust off my old knowledge of confidence intervals from uni and ran into a sticky situation - i'm not certain how to work out the 95% confidence interval for some data in terms of a percentage.

    I've simplified the problem below.

    Lets say I want to work out the average percentage of household spend that is spent in the garden in a particular village. The data I have is for say 10 households, each with different household spends, and splits there household spends into "Garden" and "Non Garden", by percentage. See attached spreadsheet for example.

    I have no information about the population, only about the sample.

    How do I work out the 95% confidence interval for this? I started looking at confidence intervals for proportions but It doesn't seem to fit ideally as a simple survey of pass/fails. Should I be calculating a regular confidence interval, using the percentage simply as the number/result?

    I know the sample size is very small so think I should be looking at student t distributions - I then started getting confused and having nightmares of 2nd year uni stats. Any pointers please?

    Any help is much appreciated.
    Attached Files
  1. File Type: xlsx SAMPLE PROP CONF INT PROBLEM.xlsx (9.6 KB, 27 views)
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    surely you can just do a chi squared analysis of the mean of the sample?
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    (Original post by Darth_Narwhale)
    surely you can just do a chi squared analysis of the mean of the sample?
    Perhaps, yes - but this is actually to deal with some rules set down that say a confidence interval must be given.
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    For any confidence interval, what you are saying is: I have a model (say the percentage of income... is normally distributed around a mean of ... with a s.d. of ...), and then you can give a confidence interval from that. So I guess my question is, what is your model?
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    (Original post by Darth_Narwhale)
    For any confidence interval, what you are saying is: I have a model (say the percentage of income... is normally distributed around a mean of ... with a s.d. of ...), and then you can give a confidence interval from that. So I guess my question is, what is your model?
    The example I posted is grossly simplified, let's say I'm complying with a councils's rule that says instead of reporting every household's garden spend individually, you can perform a sampling exercise to get a weighted average spend % and apply this to the entire village's spend to work out the entire village's garden spend.

    The rules say you can only do this if the weighted average falls withing a 95% confidence interval of plus/minus 3%.

    So, how would one work out the 95% confidence interval for a weighted average of percentages? (Each household sampled has their total spend and garden spend in £ as part of the data set)
 
 
 
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