Question

A chemist examines 15 geological samples for potassium chloride concentration. The mean potassium chloride concentration for the sample data is 0.376 cc/cubic meter with a standard deviation of 0.0012. Determine the 95% confidence interval for the population mean potassium chloride concentration. Assume the population is approximately normal. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

Answer:

$0.376-2.145\frac{0.0012}{\sqrt{15}}=0.375$    

$0.376+2.145\frac{0.0012}{\sqrt{15}}=0.377$    

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

$\bar X=0.376$ represent the sample mean for the chloride concentration

$\mu$ 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:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (1)

Since we need to find the critical value first we need to begin finding the degreed of freedom

$df=n-1=15-1=14$

The Confidence is 0.95 or 95%, the significance would be $\alpha=0.05$ and $\alpha/2 =0.025$, and the critical value for this case with a t distribution with 14 degrees of freedom is $t_{\alpha/2}=2.145$

And the confidence interval is:

$0.376-2.145\frac{0.0012}{\sqrt{15}}=0.375$    

$0.376+2.145\frac{0.0012}{\sqrt{15}}=0.377$    

And we are 95% confident that the true mean of chloride concentration is between 0.375 and 0.377 cc/ cubic meter