The standard error is computed with two approaches.

sqrt ( p1 hat *(1- p1 hat)/n1+ p2 hat* (1-p2 hat)/n2)

Or

sqrt( phat *(1-phat)/n) where phat is the common proportion.

phat = 0.383994=0.384

n =1362.

If we follow the first route

standard error = 0.025157=0.025

if we follow the second route

standard error = .013179= 0.013

I do not know what your instructor has taught or what is fed into computer.

Hence i am providing both the formulas and the results.

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