Question

Using a graphing calculator find the value of tα/2 for a 95% confidence interval when the sample size is 24.

Answer 1

We will, first of all, calculate the alpha level

`\alpha=1-confidence\text{ interval}`

The given confidence interval is

`=95\text{ \%=0.95}`

Therefore, the alpha level will be

`\begin{gathered} \alpha=1-0.95 \\ \alpha=0.05 \end{gathered}`

for,

`\begin{gathered} (\alpha)/(2,) \\ we\text{ will have} \\ (\alpha)/(2)=(0.05)/(2)=0.025 \end{gathered}`

The degree of freedom is

`\begin{gathered} df=n-2 \\ \text{where n=sample size}=24 \\ df=24-2 \\ df=22 \end{gathered}`

Using a graphing calculator,

`t_{(\alpha)/(2)}=2.073873`

Hence ,

T(ALPHA/2) VALUE= 2.073873