Can I use paired sample t-test for the following problem?

Question

Suppose there is an experiment that in each trial returns a two vector of probabilities of size $n$. In each trial I select uniformly a number from ${1,\cdots, n}$ and compare that element in this two vectors. I want to see if in a large number of trials, that randomly selected element of first vector is greater than the second one. For this I am planning to compare their mean values according to paired sample $t$-test. I know that the vector elements have specified variance and expected value. With this information is it justified to use this hypothesis test?

Thank you.

Is there an expectation that the two values will be positively correlated? — Jeremy Miles, Apr 01 '13 at 22:09
See also this question http://stats.stackexchange.com/q/47453/16974 on the impact of using a paired t-test for unpaired data (which is your situation), and the impact of using an unpaired t-test for paired data. — James Stanley, Apr 02 '13 at 21:23

score 1 · Accepted Answer · answered Apr 02 '13 at 20:46

If there is no expectation of a correlation between the values in the 'pairs' then using a paired t-test will reduce the power of the t-test by reducing the degrees of freedom without a compensating reduction in the variance of the measure.

(If the values are probabilities then they cannot be normally distributed and a standard t-test may be inappropriate. However, if the sample size is large enough the t-test is quite robust to departures from normality, particularly if the actual distribution is symmetrical and the two distributions have similar widths.)

Can I use paired sample t-test for the following problem?

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