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A researcher examines 27 sedimentary samples for bromide concentration. The mean bromide concentration for the sample data is 0.383 cc/cubic meter with a standard deviation of 0.0209. Determine the 90% confidence interval for the population mean bromide 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.

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Answer:

Critical value:
z = 1.645

The 90% confidence interval for the population mean bromide concentration is (0.376, 0.39).

Explanation:

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


\alpha = (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. This value of z is the critical value

Now, find M as such


M = z*(\sigma)/(√(n))

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


M = 1.645*(0.0209)/(√(27)) = 0.0066

The lower end of the interval is the mean subtracted by M. So it is 0.383 - 0.0066 = 0.376 cc/cubic meter

The upper end of the interval is the mean added to M. So it is 0.383 + 0.0066 = 0.39 cc/cubic meter

The 90% confidence interval for the population mean bromide concentration is (0.376, 0.39).

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