Felipe wants to grow his own jalapeño peppers so that he can make fresh salsa. When he picked out his seedlings at the plant nursery, he was told that jalapeño peppers of this variety reach an average length of $2.75\text{ inches}$ with a standard deviation of $0.25\text{ inches}$.

Felipe thinks that the average length of his peppers is less than $2.75\text{ inches}$ and decides to do a test. Assume all of the appropriate conditions have been satisfied.

If Felipe finds that $8$ randomly selected peppers have an average length of $2.625\text{ inches}$, is this enough evidence to suggest that his peppers are shorter on average than what was advertised to him?

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