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.

  • $\begingroup$ 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

An example calculation assuming no distribution is given at:


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.

  • $\begingroup$ 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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