Answer:
The 95% CI for the true average porosity of a certain seam if the average porosity for 25 specimens from the seam was 4.85 is between 4.54 and 5.16.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
![\alpha = \frac{1-0.95}{2} = 0.025](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B1-0.95%7D%7B2%7D%20%3D%200.025)
Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so ![z = 1.96](https://tex.z-dn.net/?f=z%20%3D%201.96)
Now, find the margin of error M as such
![M = z*\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which
is the standard deviation of the population and n is the size of the sample.
![M = 1.96*\frac{0.78}{\sqrt{25}} = 0.31](https://tex.z-dn.net/?f=M%20%3D%201.96%2A%5Cfrac%7B0.78%7D%7B%5Csqrt%7B25%7D%7D%20%3D%200.31)
The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.31 = 4.54.
The upper end of the interval is the sample mean added to M. So it is 5.85 + 0.31 = 5.16.
The 95% CI for the true average porosity of a certain seam if the average porosity for 25 specimens from the seam was 4.85 is between 4.54 and 5.16.