这个英文句子里的that起什么作用

这个英文句子里的that起什么作用He rations hope and vision,applies it sparingly,like his hair dye--convinced,rightly,that if they hire him for the job,the American people will be looking for a grownup,pragmatic,cut-the-deal president.that if里的that可以去掉吗?如何翻译?