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

Answer:

The answer is "(4.518, 5.182)"

Step-by-step 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

$=\bar{x}\pm Z_{\frac{0.05}{2}} \frac{\sigma}{\sqrt{n}}\\\\=4.85\pm 1.96 \frac{0.74}{\sqrt{19}}\\\\=4.85\pm 0.332\\\\=(4.518, 5.182)$

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