We will calculate the alpha level
[tex]\begin{gathered} \alpha=1-confidence\text{ interval} \\ \end{gathered}[/tex]The confidence interval given is
[tex]C\mathrm{}I=90\text{ \%=0.90}[/tex]Therefore, the alpha value will be
[tex]\begin{gathered} \alpha=1-0.90 \\ \alpha=0.10 \end{gathered}[/tex]Therefore,aplha/2 will be
[tex]\begin{gathered} \frac{\alpha}{2}=\frac{0.10}{2} \\ \frac{\alpha}{2}=0.05 \end{gathered}[/tex]Let's calculate the degree of freedom(df)
[tex]\begin{gathered} df=n-2 \\ \text{where n=sample size=6} \\ df=6-2 \\ df=4 \end{gathered}[/tex]Using the graphing calculator, t(alpha/2) will =2.131802
