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" Prof. J conducts a hypothesis test on whether the proportion of all students who bike to school (denoted as p) equals 30%. Specifically, Prof. J has H0: p=0.3 versus HA: p≠0.3. He obtains a P-value of 0.01.

On the other hand, Prof. S 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. J's result, will the null hypothesis of Prof. S's test be rejected? "

Yes, no, or do we have enough info to tell? And most importantly, why?

I'm not sure how to work through this problem, even though I think I'm somewhat familiar with the underlying concepts. It's just tricky for me to apply them and piece it all together.

Here's what I got so far:

To my understanding, Prof. J is conducting a two-tailed population proportion test (p ≠ p0), with the null hypothesis for the parameter p = 0.3. The P-value is twice the area of one of the tails (as the tails are equal, so each tail has P-value of 0.05).

Prof S. is testing an alternative hypothesis, right-tailed test : p > p0. His significance level of 0.10 indicates a 10% probability that the results are due to chance (i.e. null hypothesis).

Thank you in advance!

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  • $\begingroup$ Part of the problem is the mischaracterization of the p-value: once you get that straightened out, you will likely see the answer immediately. Check our some of our threads on p-values, such as stats.stackexchange.com/questions/31. $\endgroup$ – whuber Jul 27 at 18:33
  • $\begingroup$ We don't know whether Prof J observed $\hat p$ greater or less than $0.3.$ If we knew $\hat p > 0.3$ and his P-value is 10%, then his result would be useful to Prof S, testing against a right-tailed alternative. $\endgroup$ – BruceET Jul 27 at 21:32

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