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# Find The critical value(s) and rejection region(s) for the type of t-test with level of significance $\alpha$ and sample size n. Left-tailed test, $\alpha=0.05, n=48$

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Given:

\begin{align*} n&=\text{Sample size}=48 \\ \alpha&=\text{Significance level}=0.05 \\ &\text{Right-tailed test} \end{align*}

The critical values can be found in Student $t$-distribution table in the appendix in the row of $df=n-1=48-1=47$ (since the table does not contain a row $df=47$, we use the nearest smaller degrees of freedom $df=45$ instead) and the column of $\alpha=0.05$ (one tail):

$t=-1.679$

The rejection region then contains all values below $-1.679$.

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