Birth: "Massachusetts, Town Clerk, Vital and Town Records, 1626-2001," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:Q29P-Q7NN : 13 July 2016), Benj. Hoag in entry for Esther Hoag, 03 May 1734; citing Birth, Amesbury, Essex, Massachusetts, United States, , town clerk offices, Massachusetts; FHL microfilm 893,105. as found at 
It may be possible to confirm family relationships with Esther by comparing test results with other carriers of her ancestors' 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 DNA with Esther: