You have a strong sense of responsibility, don't you?
You're a very conscientious person, aren't you?
この場合、次のように言えますよ。
ーYou have a strong sense of responsibility, don't you?
「あなたは責任感が強いんですね」
to have a strong sense of responsibility で「責任感が強い」と言えます。
ーYou're a very conscientious person, aren't you?
「あなたはとても責任感が強い人なんですね」
a very conscientious person で「とても責任感が強い人」
conscientious は「誠実な・念入りな・真面目な」などの意味があり、responsible の同意語です。
ご参考まで!