It sounds like you are trying to test the null hypothesis #H_{0}:p=0.45# against the two sided alternative #H_{1}:p!=0.45#, based on a sample size #n=200#, a sample proportion #\hat{p}=0.57#, and a significance level #alpha=0.04#.
Assuming the null hypothesis is true, the standard deviation of the sampling distribution of #\hat{p}# is #\sigma_{\hat{p}}=\sqrt{\frac{p_{0}(1-p_{0})}{n}}=\sqrt{\frac{0.45\cdot 0.55}{200}}=sqrt(0.0012375}\approx 0.03517812#.
Hence, the value of the test statistic is #z=\frac{\hat{p}-p_{0}}{\sigma_{\hat{p}}}\approx \frac{0.57-0.45}{0.03517812}\approx 3.41#.
The #P#-value of the test is therefore #2 \cdot \mbox{Pr}(Z\geq 3.41)\approx 0.0006 < alpha#.
We therefore reject the null hypothesis. We have strong evidence against the assumption that #p=0.45#. Therefore we think #p!=0.45#. It seems that the 45% statistic is incorrect.
