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Researchers wanted to test whether right-handed individuals earn more than left-handed individuals.

A survey of $60$ randomly selected left-handed individuals found that they had an annual income of $\$42{,}345$ and standard deviation of $\$7{,}450$.

The same survey found that $50$ randomly selected right-handed individuals had an annual income of $\$46{,}812$ and standard deviation of $\$5{,}943$.

If researchers concluded that this data gives significant evidence right-handed individuals earn more, they

A

Are correct at the $5\%$ level, but not at the $1\%$ level.

B

Are correct at the $10\%$ level, but not at the $5\%$ level.

C

Risk a small chance of committing a type I error.

D

Risk a small chance of committing a type II error.

E

Should have surveyed more people to get a $p$-value significant at $1\%$.

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