A student asked the other day, “Why can't you just do P1 - P2 instead of a Chi Square test for association?” And the an

[answerhappygod]

A student asked the other day, “Why can't you just do P1 - P2
instead of a Chi Square test for association?” And the answer
is “You can, if P1 - P2 is appropriate.” To look
more closely at this, we will employ a hypothetical poll, where the
input and output are both binomial “yes/no” type questions.
In our poll, there are 1000 subjects who each identify as male
or female. We ask each one a yes/no question. The results are
summed up in the following two way table.
Gender/Response
Yes
No
Total
Male
90
310
400
Female
110
490
600
Total
200
800
1000
Ho: Gender and response are independent
Ha: Gender and response are not independent
p-hat male:
p-hat female:
p-hat “uber”:
SE p-hat(male) –
p-hat(female) : (keep at least 5 decimal places )
Test Statistic: (5
decimals):
p-value: (whatever StatKey gives)
Take the test statistic from part one
and square it. Compare your answer to the result of part 2a)