Suppose that we want to test a claim that U.S. college students spend an average of 21 hours per week studying for their classes. We collect a sample and find that the mean number of hours spent studying per week in that sample is 19.8. After carrying out a 6-step hypothesis test with a significance level α of 0.05, we decide that we cannot reject the claim. Part (a) Is it possible that the p-value for the above test is 0.03? Please answer “yes” or “no,” then explain your answer. Part (b) Is it possible that the p-value for the above test is 0.2? Please answer “yes” or “no,” then explain your answer. Part (c) Is it possible that the p-value for the above test is 1.96? Please answer “yes” or “no,” then explain your answer.

All of these are answered from the same basic principle. The p-value, in essence, gives the probability that the sample mean you obtained occurred by chance assuming that the null hypothesis is correct.
A small p-value indicates that getting such a sample is unlikely.
We compare the p-value to alpha , which is our confidence level. alpha is the likelihood of committing a Type I error -- rejecting a true null hypothesis. If the p-value is less than alpha we are provided evidence that the sample obtained would not have happened by chance and thus we should reject the null hypothesis.
Given alpha=.05:
(a) If .03.05
(b) Sure. Since p>.05 we would not reject the null-hypothesis.
(c) No. The p-value is a probability and thus 0<=p<=1
http://mathworld.wolfram.com/HypothesisTesting.html