I want to construct the following hypothesis test:
$$H_0: \theta < \theta_0 \ \mathrm{vs.} \ H_1: \theta \geq \theta_0.$$
My idea was that the one-sided Wald test is equivalent to testing whether $\theta_0$ is contained in the following confidence interval (if not then reject the null hypothesis):
$$(-\infty,\hat{\theta} - z_{\alpha} \hat{\mathrm{se}}(\hat{\theta}))$$
but I am not sure whether this makes sense. And by the way, $\theta$ is the Binomial parameter $p$ so $\theta \in [0,1]$.