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.