half convinced and half doubtful; having doubts about something while not completely rejecting it (idiomatic four-character phrase).
彼の成功話は少し大げさに聞こえて、私は半信半疑だった。
His stories of success sounded a bit exaggerated, and I was half convinced, half skeptical.
新しいダイエット法の効果に半信半疑で試してみたが、効果が出た。
I tried the new diet method with some skepticism, but it worked.
噂話を聞いても、まずは半信半疑で情報の真偽を確かめるべきだ。
Even when you hear gossip, you should be half doubtful at first and check the truth of the information.