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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...

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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