Answer:
[tex]150-2.797\frac{35}{\sqrt{25}}=130.421[/tex]
[tex]150+2.797\frac{35}{\sqrt{25}}=169.579[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=150[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean
s=35 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)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=25-1=24[/tex]
Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex] and the critical value for this case [tex]t_{\alpha/2}=2.797[/tex]
Now we have everything in order to replace into formula (1):
[tex]150-2.797\frac{35}{\sqrt{25}}=130.421[/tex]
[tex]150+2.797\frac{35}{\sqrt{25}}=169.579[/tex]
