Ann (possibly this is Alice, grand-daughter, but if so then she is a year older than we have here).
Sources
↑ Massachusetts, Town and Vital Records, 1620-1988: Deerfield Vital Record Transcripts, p. 130 (Ancestry.com)
"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MCBP-F86 : 12 April 2016), Ann H Bates in household of Daniel D Bates, Manlius, Onondaga, New York, United States; citing family 1139, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
"New York State Census, 1855," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:K6QV-MCS : 6 February 2018), Ann Bates in household of Daniel Bates, E.D. 1, Manlius, Onondaga, New York, United States; citing p. 373, line #14, family #3, county clerk offices, New York; FHL microfilm 870,756.
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DNA Connections
It may be possible to confirm family relationships with Anna by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Anna: