How to do large sample tests of significance for differences between two proportions

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AP Statistics › How to do large sample tests of significance for differences between two proportions

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We are comparing the Democratic percentage of Detroit to the Democratic percentage of Dallas.

In Detroit, we sampled 300 people and 208 were Democrats (.693)

In Dallas, we sampled 350 people and 265 were Democrats (.757)

What is the p-value for the .064 difference?

(Assume a 2-tailed test.)

.0688

.0344

.0244

.0765

.0577

Overall percentage =

$SD=\sqrt{(.728)*(.272)*(1/300 + 1/350)} = .035$

$Z_{1.82}=.9656; 1-.9656=.0344$

.0344 is for one tail, so .0688 is for both tails.

(Percentages are different at the .9312 level.)