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ahrayia [7]
3 years ago
9

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.
Mathematics
1 answer:
NikAS [45]3 years ago
7 0

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

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