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It could be one of several things, a system reset, a firmware update but it sounds like a screen cable has become disconnected or similar fault. Before doing anything, is it still under warranty, if so its best to go back to the vendor or leapfrog and request an exchange. Here's the url to their support page.
seems like a bad connection inside maybe the ribbon cable is a little loose (from being dropped, movement from playing etc...) if its under warranty i'd send it in to get fixed if its not then you have nothing to lose taking it apart yourself (with no power supplied to it of course) and see if you can find anything loose. If the game is still visible and the wires are seperate i would check the ones leading to your backlight.
I'm really not sure at this point -- there aren't to many things you can do with a leapster to fix the display....how old is it? Wondering if Leapster will do anything for you if it's too old to exchange at a store. Typically screens turn white if they need to be refreshed OR if they have overheated or been left in a car or a hot place -- because the lcd gets messed up in extreme heat. Wished I could help you more then that...but calling leapster sounds like your only option right now..unless exchanging at the store is possible.
Carry out the test. The calculator will display a p= value (or if you draw it - it will be the shaded area). This is the type one error. Why? Well if H0 is true then your t-test will come from this distribution. Think of the bell shape as a histogram - you have one value you are comparing to it. Is this value typical of this "histogram"? If the value is near the centre of the bell it is reasonable that it came from it. If it is in the extreme it probably didn't and so we reject H0. The type one error is the probability that we reject H0 given that it is true. H0 assumes the t value comes from this distribution - so it is the probability of getting this value or something more extreme. (i.e. the shaded area. Incidently this is the same way of finding the type one error for any test.