Basic Hypotheses testing with Binomial.

The poverty rate in a city is thought to be 0.15. After some poverty reduction programs were introduce a random sample of 400 inhabitants was taken and 50 of them were deemed to be in poverty. Test the hypothesis that the policies were a failure by performing a one sided lower tailed test of population proportions setting the size of the test at 5% (ie α=0.05).
I did some work but not sure if it's correct.
x~Binomial(400,0.125) then the variance= 400*0.125*0.875 = 43.75.
Then P(Cl<X<Cu) = 95% -> C=0.15±1.96*sqr(43.75/400)

I'm not sure if I should use 0.125 as p to calculate the variance or 0.15 and if C=0.15... or C=0.125...
Much appreciated for any reply.

\(\displaystyle H_{0}: \;\ p\geq .15\)

\(\displaystyle H_{a}: \;\ p<.15, \;\ \text{claim}\)

The critical value for a .05 alpha is 1.645

\(\displaystyle z=\frac{.125-.15}{\sqrt{\frac{(.15)(.85)}{400}}}=-1.4\)

Check the test statistic against the critical value of -1.645.

Do we reject or not reject?. What does it mean with regard to the program working?.