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Sever21 [200]
3 years ago
6

A geologist examines 14 geological samples for iron concentration. The mean iron concentration for the sample data is 0.181 cc/c

ubic meter with a standard deviation of 0.0318. Determine the 90% confidence interval for the population mean iron 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:
kykrilka [37]3 years ago
3 0

Answer:

The 90% confidence interval for the population mean iron concentration is between 0.167 cc/m³ and 0.195 cc/m³.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.645*\frac{0.0318}{\sqrt{14}} = 0.0140

The lower end of the interval is the sample mean subtracted by M. So it is 0.181 - 0.0140 = 0.167 cc/m³.

The upper end of the interval is the sample mean added to M. So it is 0.181 + 0.0140 = 0.195 cc/m³.

The 90% confidence interval for the population mean iron concentration is between 0.167 cc/m³ and 0.195 cc/m³.

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