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Answer:
The 95% CI for the true average porosity of a certain seam is (4.52, 5.18).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.77}{\sqrt{21}} = 0.33[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.33 = 4.52.
The upper end of the interval is the sample mean added to M. So it is 4.85 + 0.33 = 5.18
The 95% CI for the true average porosity of a certain seam is (4.52, 5.18).
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