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<p<.05 ` we would have rejected the null hypothesis. Since we did not reject the null hypothesis, p>.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 `

**Further Reading**