Do you reject when t = 1.85 with 20 degrees of freedom?

Question

A two-sided t-test with 20 degrees of freedom produces a test statistic of t = 1.85. The critical value at the 5% level is t{0.025,\,20} = 2.086. Do you reject the null hypothesis at the 5% level?

Accepted Answer

The rule for a two-sided test: reject H0 if t exceeds the critical value. Here t = 1.85 < 2.086, so we fail to reject H0. The statistic simply is not extreme enough: it lands inside the range of values the null can plausibly produce. Takeaway. "Fail to reject" is not proof the null is true; it means the evidence is not strong enough to overturn it. Note the t-cutoff (2.086) is stricter than the z-cutoff (1.96) because the t-distribution has heavier tails at finite degrees of freedom.

Do you reject when t = 1.85 with 20 degrees of freedom?

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