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

`0.376-2.145(0.0012)/(√(15))=0.375`

`0.376+2.145(0.0012)/(√(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

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)(s)/(√(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(0.0012)/(√(15))=0.375`

`0.376+2.145(0.0012)/(√(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