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.

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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 `

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