If you were an average person in Westeros, wouldn’t you think Tyrion is guilty?

There’s so much going against him. Tyrion probably had the strongest motive to kill Joffrey, aside from Sansa, and he also had the means to do it. It doesn’t help that Sansa disappears immediately after the poisoning. We know Tyrion didn’t do it because we see his actions firsthand, but to the average person in Westeros, he probably looks guilty. What do you think?