Answer:
[tex]t_{\alpha/2}=1.318[/tex]
And the confidence interval would be given by:
[tex]393.5-1.318\frac{50.30}{\sqrt{25}}=380.24[/tex]
[tex]393.5+1.318\frac{50.30}{\sqrt{25}}=406.76[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=393.50[/tex] represent the sample mean
[tex]\mu[/tex] population mean
s=50.30 represent the sample standard deviation
n=25 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
The Confidence level is 0.80 or 80%, the value of significance [tex]\alpha=0.2[/tex] and [tex]\alpha/2 =0.1[/tex], the critical value for this case would be:
[tex]t_{\alpha/2}=1.318[/tex]
And the confidence interval would be given by:
[tex]393.5-1.318\frac{50.30}{\sqrt{25}}=380.24[/tex]
[tex]393.5+1.318\frac{50.30}{\sqrt{25}}=406.76[/tex]
