How does Vera's poise and self-confidence contribute to her being believed in "The Open Window"?

First of all, Vera's poise and self-confidence perceived
by a man such as Framton Nuttel who himself lacks such things lends her a superiority. 
As superior in demeanor, she is thus somewhat intimidating to Nuttel; so, he would be
afraid to challenge what she says. For instance, when Vera tells Nuttel that he must
put up with her while he waits for Mrs. Stappleton,

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Framton Nuttel endeavored to say
the correct something that should duly flatter the niece of the moment
without unduly discounting the aunt that was to
come. 

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Also, this self-confidence lends her a maturity beyond her years; this fact adds to the
credibility factor as Nuttel may place her on a more equal plane with himself as well as
giving more faith to her "testimony" that Mr. Stappleton and his two brothers-in-law
went off for their day's shooting three years ago.  Of course, the more mature idea of
suggesting that the men left through an open window also
suggests veracity [notice the similarity to her name] to Vera's tall tale.  In addition,
her poise enables Vera to fabricate with seriousness, a fact that affects Nuttel's
credence, as well.