A researcher reports her results as: (t (62) = 3.12, p < 0.002). what does this mean

what does this mean and why? does this expression indicate that her results were statistically significant?

and also if her results were (t (33) = 0.42, p < 0.50). - what would this mean, why, and are her results statistically significant?

Please help so confused on this concept!

p is the probability of getting a more extreme result if the null hypothesis is true. If p <0.002, then the sample in question was either highly extreme (unlikely) or the null hypothesis was false (which is what you should conclude) and the results are statistically significant.

if the p-value is less than .50, then that is not an unlikely event under the null hypothesis and one cannot conclude that the results are significant.