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I have a simple random sample of size 40 which talks about no. of newspapers being sold by a particular salesboy each day. Population standard deviation is not know.

I did a normality test on this data and Anderson-darling test rejected the null hypothesis (owing to a few outliers on the right end of the curve)

So, to calculate the confidence interval, can I use t-distribution for this? If not, what other methods can be used for the confidence interval calculation?

Edit: Sorry for not specifying this earlier, I would like to calculate the confidence interval for the estimate of mean number of newspapers sold.

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  • $\begingroup$ For which parameter would you like to compute a confidence interval? $\endgroup$ – Michael M Oct 4 '15 at 11:43
  • $\begingroup$ It is for the mean number of newspapers sold. Could you please take a look now. $\endgroup$ – Bach Oct 4 '15 at 12:53
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An example calculation assuming no distribution is given at:

https://epilab.ich.ucl.ac.uk/coursematerial/statistics/non_parametric/confidence_interval.html

I'm assuming the procedure is named Wilcoxon signed rank test.

By the way, it is said that if the sample size is large enough then it is possible to use a t-test even if the sample distribution is non-normal (due to the central limit theorem). I've seen examples stating n>30 would suffice.

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  • $\begingroup$ I too have also read everywhere saying that n>30 would mean t-test is an immediate choice. But here I also have a few outliers in the data at the right end which i do not want to remove, so I guess, I should not be using t-test after all. Wilcoxon came out as an alternative in my google search, waiting to see what the folks here would suggest. $\endgroup$ – Bach Oct 4 '15 at 12:55

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