Test for significance with no comparator

Question

I have roughly 15,000 non-independent features for each of which I have a sample size of 100. For each of these feature-sample data points, I have a value of TRUE or FALSE corresponding to some status of the feature, such that for each feature, I have 100 TRUE or FALSE values.

How can I test the "trueness" of each feature and thereby determine the percentage of features with a significant TRUE value? A suitable null hypothesis may be that the feature does not have a TRUE status. My problem though is that an $\alpha$ of 0.05 corresponding to a rejection of the null hypothesis if there are >95 TRUES for a feature, seems too high. I have no reference dataset by which to make a comparison.

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UPDATE: Re: Use of Fisher's exact test.

I am not sure what parameters to use for the 2 x 2 contingency table using Fisher's exact test or chi-squared test. What would class 1, class 2, sample 1 and sample 2 be? 'TRUE count', etc.? Here are the first few rows and columns of the data:

          Sample1 Sample2 Sample3 Sample4 Sample5 Sample6 Sample7 Sample8 Sample9 Sample10
Feature1    TRUE    FALSE   TRUE    FALSE   TRUE    TRUE    FALSE   TRUE    FALSE   FALSE
Feature2    TRUE    FALSE   TRUE    FALSE   TRUE    TRUE    FALSE   TRUE    FALSE   FALSE
Feature3    TRUE    FALSE   TRUE    FALSE   TRUE    TRUE    FALSE   TRUE    FALSE   FALSE
Feature4    TRUE    FALSE   TRUE    FALSE   TRUE    TRUE    FALSE   TRUE    FALSE   FALSE
Feature5    TRUE    FALSE   TRUE    FALSE   TRUE    TRUE    FALSE   TRUE    FALSE   FALSE
Feature6    TRUE    FALSE   TRUE    FALSE   TRUE    TRUE    FALSE   TRUE    FALSE   FALSE
Feature7    TRUE    FALSE   TRUE    FALSE   TRUE    TRUE    FALSE   TRUE    FALSE   FALSE
Feature8    FALSE   FALSE   TRUE    FALSE   TRUE    TRUE    FALSE   TRUE    FALSE   FALSE
Feature9    FALSE   FALSE   TRUE    FALSE   TRUE    TRUE    FALSE   TRUE    FALSE   FALSE
Feature10   FALSE   FALSE   TRUE    FALSE   TRUE    TRUE    FALSE   TRUE    FALSE   FALSE
Feature11   FALSE   FALSE   TRUE    FALSE   TRUE    TRUE    FALSE   TRUE    FALSE   TRUE
Feature12   FALSE   FALSE   TRUE    FALSE   TRUE    TRUE    TRUE    TRUE    FALSE   TRUE
Feature13   FALSE   TRUE    TRUE    FALSE   FALSE   TRUE    TRUE    TRUE    FALSE   TRUE
Feature14   FALSE   TRUE    TRUE    FALSE   FALSE   TRUE    TRUE    TRUE    FALSE   TRUE
Feature15   FALSE   TRUE    FALSE   FALSE   FALSE   TRUE    TRUE    TRUE    FALSE   TRUE

Answer 1

What you could do is test whether some features have significantly more trues than others (or than the average). This would be Pearson’s Chi-Squared test or Fisher’s exact test.

Edit: Note that this approach somewhat contradicts your initial question, as it constructs a comparator. However, the very idea of a statistical test requires comparison.