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Suppose I conduct a hypothesis test and $H_0: \mu = 7$ and $H_A: \mu \neq 7$. Let's say the $p$-value is 0.03. Would a 95% confidence interval contain the value $7$? I think it would since alpha (which is 0.05) is higher than the $p$-value.

However, the question that is really bothering me is would I have enough information from this hypothesis test (if the only information we have is the $p$-value and hypotheses) to conclude if the value $6$ is contained in this 95% confidence interval?

I don't think I would since I have no information on the sample mean and variance.

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    Maybe ask this on stats.SE instead?2012-01-25
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    If you decide to take @Dilip up on his suggestion (a reasonable one), it is best to flag your post and ask that it be migrated instead of, e.g., creating another identical copy over there. Cheers. :)2012-01-25
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    I think I'll leave it here. It's probably not too complicated. I'm just a bit rusty on the theory behind hypothesis testing.2012-01-25
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    The main problem at this point is that the question as stated is a bit ill-posed. Is this for a normal model? What procedure are you using to construct the confidence interval? What test was used to obtain the stated $p$-values and how does it relate to the construction of the CI? Do you know the sample size? These are questions to help you begin the thought process and to consider what information would be relevant to even have a chance at arriving at a concrete answer.2012-01-25
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    Unfortunately, the only data I have available are the hypotheses and the p-value, which leads me to conclude I don't have enough information to conclude the second assertion I made. The first one, however, I think I am correct about since the p-value is less than 0.052012-01-25
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    I would think logically about the reasoning first (what does it mean if the $p$-value is 0.03?) and maybe consider a very simple example. Say, a sample of size one from a normal model with unknown mean and variance one...2012-01-25

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