Answer:
a) ![z = 1.645](https://tex.z-dn.net/?f=z%20%3D%201.645)
b) Lower endpoint: 0.422cc/m³
Upper endpoint: 0.452 cc/m³
Step-by-step explanation:
Population is approximately normal, so we can find the normal confidence interval.
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
![\alpha = \frac{1-0.9}{2} = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B1-0.9%7D%7B2%7D%20%3D%200.05)
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
. This is the critical value, the answer for a).
Now, find 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 = 1.645*\frac{0.0325}{\sqrt{12}} = 0.015](https://tex.z-dn.net/?f=M%20%3D%201.645%2A%5Cfrac%7B0.0325%7D%7B%5Csqrt%7B12%7D%7D%20%3D%200.015)
The lower end of the interval is the sample mean subtracted by M. So it is 0.437 - 0.015 = 0.422cc/m³.
The upper end of the interval is the sample mean added to M. So it is 0.437 + 0.015 = 0.452 cc/m³.
b)
Lower endpoint: 0.422cc/m³
Upper endpoint: 0.452 cc/m³