Respuesta :
Answer:
[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]
[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=32.9[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s=4.9 represent the sample standard deviation
n=8 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=8-1=7[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this cae would be [tex]t_{\alpha/2}=2.365[/tex]
Now we have everything in order to replace into formula (1):
[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]
[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]
