It would still be simpler for you to link to a credible source. A bit strange that you seem uninterested in doing so, and prefer to tell people to do their own experiments, in this case one that requires an extra phone and a week of time.

Batteries naturally drain slowly when not used. What would this little experiment prove, exactly?

Interesting, but you should probably use a control. Two phones, same hardware, same software. One inside the faraday cage, one outside, both in the same room with the same conditions otherwise.

Repeat the experiment a few times. Then cross over: liberate the caged phone, cage the free phone, and repeat the experiment a few more times. Or alternate the phones' positions between experiments. This mitigates hardware and software differences that might've been overlooked (such as a faulty battery, etc).

Analyze the results, draw your conclusions, publish, and encourage others to reproduce.