Fran,
I am so sorry to hear that your friend Mei is not willing to attend a English competition.Here I have some advice that you can use to persuade her.Firstly, you should detail the advantage of attending the competition like testing the ability of English,building confidence to learn English and so on.Secondly,you'd better contain her family and let her family persuade her,which make great influence on her.Good luck!
yours,
******