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Degrees of Freedom and Statistical Significance

APSTAT-BYPYGG

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, df. If the true df should have been higher than the df she had used in her calculation, would her results still be statistically significant?

A

No, using a higher value for df would result in a higher $p$-value.

B

Maybe, using a higher value for 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 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 df would result in a lower $p$-value.

E

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