given,

for western residients

population=1020

probability(p1)=0.43

for northeast residients

population=920

probability(p2)=0.5

P=(p1*n1+p2*n2)/(p1+p2)

=0.463

Q=1-P=0.536

Z at 98% level=2.326

standard error=(N*P*Q)^0.5/N=21.9/1940=0.011(mistakenly done for other question, this is the answer for your standard error question)

Z=(p1-p2)/(P*Q(1/n1+1/n2))^0.5=1.919

Z calculated < Z at 98% llevel

both are significantly same

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