In short: typical alpha is 0.05, so a p-value < 0.05 is considered "statistically significant" and the results are not attributable to random chance in a t-test. An unpaired t-test compares two populations, and a p-value below the alpha level indicates that differences are not due to random chance.

Take everything with a grain of salt, though. Low sample sizes dramatically change how test statistics produce results. P-value hacking is the practice of eliminating data from an experiment to produce statistically significant results or otherwise altering the data by adding buffers to ensure that a result confirms a belief a researcher has.

Given a statement and a sample with a mean and standard deviation, what is the probability that you manage to choose a sample with that mean and SD, assuming the statement is true?

For example, my statement is the average weight of chicken an american eats every month is 20 pounds and my sample gives me a mean of 16 and SD of 4. The p value is the probability of choosing a group of people who eat on average 16 pounds of chicken every month if the REAL mean is actually 20.

Edit to answer question: The p value doesn't "care" about the sample size - it is adjusted and remains accurate. And so if the p value if high for the sample in the study, that means it is a likely occurrence and the result is not very noteworthy.