Answer:
Critical value is 1.318 and the confidence interval is 29.357 to 33.042
Step-by-step explanation:
n = 25
x = 31.2
s = 6.99
Degree of freedom = n-1= 25-1 =24
Confidence level = 0.8
So, α = 1- 0.8= 0.2
t critical = [tex]t_{\frac{\alpha}{2},df}=t_{\frac{0.2}{2},24}=t_{0.10,24}=1.318[/tex]
Formula of confidence interval : [tex]\bar{x}-t_{\frac{\alpha}{2},df} \times \frac{s}{\sqrt{n}}[/tex] to [tex]\bar{x}+t_{\frac{\alpha}{2},df} \times \frac{s}{\sqrt{n}}[/tex]
Confidence interval : [tex]31.2-1.318 \times \frac{6.99}{\sqrt{25}}[/tex] to [tex]31.2+1.318 \times \frac{6.99}{\sqrt{25}}[/tex]
Confidence interval : [tex]29.357[/tex] to [tex]33.042[/tex]
Hence critical value is 1.318 and the confidence interval is 29.357 to 33.042
