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Lauren conducted a one-sample $t$-test for a population mean and her results were found to be statistically significant at the $\alpha=0.05$ level.

Later, she realized that she had calculated the $p$-value using the wrong value for degrees of freedom, $\text{df}$. If the true $\text{df}$ should have been higher than the $\text{df}$ she had used in her calculation, would her results still be statistically significant?

A

No, using a higher value for $\text{df}$ would result in a higher $p$-value.

B

Maybe, using a higher value for $\text{df}$ would result in a higher $p$-value, but the $p$-value may still be less than $0.05$.

C

Maybe, using a higher value for $\text{df}$ would result in a lower $p$-value, but the $p$-value may then end up being too low for the results to be considered statistically significant.

D

Yes, using a higher value for $\text{df}$ would result in a lower $p$-value.

E

It depends on whether Lauren was using a one-sided or two-sided alternative hypothesis.

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