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# Stats help please - Confidence Interval when dealing with percentages watch

1. 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.

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
2. SAMPLE PROP CONF INT PROBLEM.xlsx (9.6 KB, 27 views)
3. surely you can just do a chi squared analysis of the mean of the sample?
4. (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.
5. 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?
6. (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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Updated: January 27, 2017
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