Which Statistical test should I use

[Link]

I have a number series ranked from largest to smallest in descending order from 10 - 1. the sample is assumed to be large enough to be normally distributed. If I pick say the 8th number from the top, which statistical test should I use to calculate the probability/C.I that the number picked is larger than a certain number, say 9?

It can be assumed that the mean and standard deviation of the sample is known

 

[chiro]

Hey Link.

The first thing to do is to estimate the population mean and variance. If you are assuming a normal distribution, you can use the normal estimator for the mean and the chi-square estimator for the variance.

Once you have these estimators, you'll probably be choosing your point estimate (but remember the estimate is an uncertain thing so you will only get one out of very many: infinitly possible means both positive and negative and infinitly many variances greater than 0).

Then once you find an estimate to use for your population mean and variance, you use this information to get the final probability. The probability will correspond to whatever number you are picking, which will be in terms of standard deviations from the mean when dealing with a normalized distribution (which is used to do probability calculations for any normal).

It sounds like you haven't done much in the way of statistics, so look up estimators for normal distributions and how to estimate the mean and variance of the population of a normal distribution given a sample that assumes normality.

You should also probably inform the readers here why you assume its normal. The fact is that it may not be normal and that the assumptions you have do not reflect the reality of the data.

One test that is popular for checking whether something is normal under a measure of uncertainty is the Shapiro-Wilk test that can be done in any common statistics package, and you can use the same package to do the estimator calculations for you as well.