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So after doing some research, people tend to confuse as to what the P-value actually stands for and results in wrong interpretation of examples. Take this one:

Prof. Johnson conducts a hypothesis test on whether the proportion of all UBC students who bike to school equals 30%. Specifically, Prof . Johnson has H0 : p = 0.3 versus HA : p ≠ 0.3 .

He obtains a P-value of 0.01. On the other hand, Prof . Smith would like to test if there is sufficient evidence to support that p is greater than 0.3 at the 10% significance level. Based on Prof. Johnson's result, will the null hypothesis of Prof. Smith's test be rejected?

So I'm not sure if this P-value in this context justifies rejecting the null hypothesis because we don't know the direction of the P-value no? I understand the P-value should be cut in half to accommodate the 1-tailed test in this case

Any help is appreciated.

Bill Cogn
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    I think it would be sufficient if we knew that the proportion in Prof. Johnson's sample is greater than 0.3. – Gribouillis May 12 '23 at 11:22
  • @Gribouillis That's what I'm hesitant on, we don't know that. All we can assume is Prof's first hypothesis test. I'd conclude that there is insufficient information to tell, which is an option for the answer. – Bill Cogn May 12 '23 at 11:26
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    We could as well ask if there is sufficient evidence to support that $p$ is smaller than $0.3$ at the 10% significance level. The answer must be the same as far as we know, so it would be a logical contradiction to reject the hypothesis. – Gribouillis May 12 '23 at 11:31
  • @Gribouillis I figured thank you for this conversation, very helpful – Bill Cogn May 12 '23 at 11:39

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