# Why is p-value 0 although proportion is higher than threshold?

In the finalAnalysisReport.txt (the result file of NIST tests), there are several columns including P-VALUE and PROPORTION.

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 P-VALUE PROPORTION STATISTICAL TEST

Some tests have * near them. Apparently, * means that test failed. When I look at those lines, some of them have enough proportions while their P-value is 0.

For example:

4 3 9 0 17 0 0 15 0 0 0.000000 * 48/48 Rank

or

9 0 3 4 2 0 4 1 11 14 0.000000 * 47/48 LinearComplexity

On the bottom of the file, it is written that:

The minimum pass rate for each statistical test with the exception of the random excursion (variant) test is approximately = 45 for a sample size = 48 binary sequences.

In other words, their proportions are higher than threshold, but they failed due to p-value. I was wondering why this happens.

Furthermore, as this is the NIST test on my PUF design, how I can I understand the issues, so I can fix them and the PUF output passes the tests.