Film with terminally ill woman and ping pong ball

[Swithin]

I posted this question when I first joined this board, around 2006,  but didn't get an answer. Trying again, since we have a new crop of intelligentsia here.

When I was very young (it would have been the 1950s), my grandmother took me to a film in which a woman thinks she's terminally ill. She has a ping pong ball that she thinks is lucky and will make her well -- or something like that.

At the end of the film, she is well and realizes the ping pong ball had nothing to do with it. In the last scene, she flings the ball away. Any ideas as to what film this might be? I used to think it was a Susan Hayward movie, but I've had no luck going through her film list, so probably not.