Question

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.74. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (Round your answers to

Answer 1

The answer is "(4.518, 5.182)"

Explanation:

`\sigma = 0.74`

The aveage porosity for a sample of
`n = 19` specimens is

`\bar{x}=4.85`

Thus, the
`95\%` confidence interval for the true mean is

`=\bar{x}\pm Z_{(0.05)/(2)} (\sigma)/(√(n))\\\\=4.85\pm 1.96 (0.74)/(√(19))\\\\=4.85\pm 0.332\\\\=(4.518, 5.182)`

Therefore, one can state that the true average porosity will lie between 4.518 and 5.182 with the 95\% confidence.