The standard error is computed with two approaches.
sqrt ( p1 hat *(1- p1 hat)/n1+ p2 hat* (1-p2 hat)/n2)
sqrt( phat *(1-phat)/n) where phat is the common proportion.
phat = 0.383994=0.384
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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