" 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!