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Everyone who shows magical ability before their eleventh birthday will automatically gain a place at Hogwarts; there is no question of not being ‘magical enough’; you are either magical or you are not. There is no obligation to take up the place, however; a family might not want their child to attend Hogwarts.
On a related note, I have added some information on Squibs in the ‘Extras’ Section (Miscellaneous).