Note the different birth dates given in the sources.
Sources
James Savage, John Farmer, Orrando Perry Dexter, Genealogical Dictionary of the First Settlers of New England. Vol. D-J. Little, Brown, 1860 - New Englan. pp.348-349.[1]
"Massachusetts Births and Christenings, 1639-1915," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:VQD9-95R : accessed 9 February 2016), Anthony Hancock in entry for Mary Hancock, 17 Dec 1701; citing WRENTHAM,NORFOLK,MASSACHUSETTS, ; FHL microfilm 0253249 V. 1.
"Massachusetts Marriages, 1695-1910," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FCHV-6PL : 9 February 2018), Michal Johnson and Mary Hancock, 1727; citing reference ; FHL microfilm 14,767.
Find A Grave, database and images, accessed 25 December 2018, memorial page for Mary Hancock Johnson (19 Dec 1701–1766), Find A Grave: Memorial #49008155, citing Hampstead Center Cemetery, Hampstead, Rockingham County, New Hampshire, USA ; Maintained by Harvey (contributor 46879971) .
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DNA Connections
It may be possible to confirm family relationships with Mary 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 Mary: