This study carries all sorts of biases if the idea is to gauge how teens really feel without their smartphones. What it tells however is that teens have this idea that they spend too much time on their smartphones.
It would be interesting to conduct a proper experiment. For example, have a randomly selected group of teens do some activity where they are allowed to keep their phones, and another group where they are not. And then ask general questions about well being without telling them it is about smartphones, and then, see the differences. A weaker measurement could be by finding correlation between mood and whether or not a place allows smartphones or has network.
And now see if the results match the questionnaires. So see if teens really feel more peaceful (or anxious) when they don't have their smartphone, or if that's just what they want to believe (or want you to believe).