Respuesta :
Answer:
[tex]9.9-2.14\frac{0.30}{\sqrt{15}}=9.734[/tex]
[tex]9.9+2.14\frac{0.30}{\sqrt{15}}=10.066[/tex]
Step-by-step explanation:
Information given
[tex]\bar X= 9.9[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=0.3 represent the sample standard deviation
n=15 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=15-1=14[/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 wuld be [tex]t_{\alpha/2}=2.14[/tex]
Now we have everything in order to replace into formula (1):
[tex]9.9-2.14\frac{0.30}{\sqrt{15}}=9.734[/tex]
[tex]9.9+2.14\frac{0.30}{\sqrt{15}}=10.066[/tex]
