Question: Max likes to keep track of birthdays of people he meets. He has 170 birthdays listed on his birthday calendar. One cold January night, he comes up with the theory that people are more likely to be born in October than they would be if all 365 days were equally likely. He consults his birthday calendar and finds that 22 of the 170 birthdays are in October.
a. Write down the null and alternative hypotheses for Max's test. Be sure to carefully specify what p represents.
b. Carry out the remaining four steps of the hypothesis test for this situation.