Hannah was born in 1734. She is the daughter of Thomas Straight, (a son of Henry Straight), and Herodias Gardiner.
Sources
Robinson, Caroline E. The Gardiners of Narragansett: Being a Genealogy of the Descendants of George Gardiner, the Colonist, 1638. 1919. Pg. 15
"Rhode Island Births and Christenings, 1600-1914", database, FamilySearch Pg. 230
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DNA Connections
It may be possible to confirm family relationships with Hannah 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 some percentage of DNA with Hannah: