Question 1137984
Ho=two proportions are equal
Ha=they aren't equal
alpha is 0.01 P{reject Ho|Ho true}
z= difference in means/SE ; SE is sqrt ((p1*(1-p1)/n1) + p2(1-p2)/n2))
reject z if |z|>1.96
phat 1=0.145 16/110
phat 2=0.26 or 13/50

NOTE: this is done with alloy1-alloy2. Change all the signs at the end.

SE is sqrt [(0.145*0.855)/110+(.26*.74)/50]=0.00497, so SE=0.070. The difference is -0.115, and the z-value is -1.64
80%CI has a z=+/-1.28
so the half-interval is 1.28*0.07=0.0896

The difference between the two is -0.115+/-0.089 or (-0.204, -0.026) meaning 0, or equality is not in the 80% CI, which is another way of saying they are from different populations.
alloy2-alloy1 CI is (0.026, 0.204)