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A local university is interested in summer earnings of its students. The data from all students over the last $10\text{ years}$ is given in the following table:

Males Females
Mean \$3,201 \$2,401
St. Dev. \$1,231 \$984



The university recently started an initiative to encourage students to find higher-paying summer jobs in line with their potential careers. A random sample of $30\text{ males}$ found a mean summer income of $\$3{,}804$ with a standard deviation of $\$1{,}240$.

Assuming females have the same standard deviation as before ($\$984$), how large of a sample mean would the female sample of size $30$ have to be in order to claim that females have benefited just as much as males from this initiative?

A

$\$2{,}474.32$

B

$\$2{,}878.88$

C

$\$2{,}938.83$

D

$\$3{,}432.10$

E

$\$3{,}804.00$

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