Respuesta :
Answer:
[tex]0.376-2.145\frac{0.0012}{\sqrt{15}}=0.375[/tex]
[tex]0.376+2.145\frac{0.0012}{\sqrt{15}}=0.377[/tex]
And we are 95% confident that the true mean of chloride concentration is between 0.375 and 0.377 cc/ cubic meter
Step-by-step explanation:
Data provided
[tex]\bar X=0.376[/tex] represent the sample mean for the chloride concentration
[tex]\mu[/tex] population mean (variable of interest)
s=0.0012 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)
Since we need to find the critical value first we need to begin finding the degreed of freedom
[tex]df=n-1=15-1=14[/tex]
The Confidence is 0.95 or 95%, the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this case with a t distribution with 14 degrees of freedom is [tex]t_{\alpha/2}=2.145[/tex]
And the confidence interval is:
[tex]0.376-2.145\frac{0.0012}{\sqrt{15}}=0.375[/tex]
[tex]0.376+2.145\frac{0.0012}{\sqrt{15}}=0.377[/tex]
And we are 95% confident that the true mean of chloride concentration is between 0.375 and 0.377 cc/ cubic meter
