Here are Ann Nelsons who lived in SD at that time, according to census:
1910
b. abt. 1895 Banger SD friend of the head of house
b. 1896 Spirit Lake Kingsbury Parent Lars Anna is daughter

b. 1896 Star Clay Coi Andrew and Cecile parents, daughter
In 1920, Ann Nelson, daughter of Lars was still single living at home.
I looked at a birth yr. of 1895 as well, because depending on Anna's birthdate in 1917, she may have not yet had her birthdate. If not, then she would have been born in 1895.
If you have a census available through your library you might look up these and get her siblings' (brothers) names and trace them forward.