Question

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.78. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 25 specimens from the seam was 4.85. (Round your answers to two decimal places.)

Answer 1

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.

Explanation:

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

`\alpha = (1-0.95)/(2) = 0.025`

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
`1-0.025 = 0.975`, so
`z = 1.96`

Now, find the margin of error 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 = 1.96*(0.78)/(√(25)) = 0.31`

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.