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The number of occurrence of a fixed template in a sequence can be used as an indication of randomness of a collection of sequences of length n. In this work, we solve the problem of determining the number of strings containing a given template for a specified number of times. We observe that these numbers are the same for any two templates having the same period. Afterwards, we propose a new family of statistical randomness tests, periodic template tests, for collections of binary sequences. We give instances of the new family for collections of sequences of length n=128, n=256, n=1024, and n=4096 to emphasize that these probabilities are feasible to compute even for n=4096. Although, the NIST test suite contains a test for the case n=1032, namely the overlapping template matching test, the probabilities stated in the NIST test suite document are valid only for one template, and the probabilities are not stated for the other templates. In this work, all other probabilities are stated.