Question

1. A machine produces metal pieces that are cylindrical in shape. A random sample of 12 metal pieces from the machine shows a mean diameter of 1.3 cm and a standard deviation of 0.05 cm. Compute a 98% confidence interval for the true average mean diameter for the metal pieces produced by the machine.

Answer 1

Standard error of sample is $s_s = \frac{\sigma}{\sqrt{n}} = \frac{0.05}{\sqrt{12}} \approx 0.0144$

From Student's distribution with 11 degrees of freedom and 98% probability get $t_{cr} = 2.718$ , therefore $\epsilon = t_{cr} s_s = 2.718 * 0.0144 = 0.039$ and the confidence interval is (1.3-0.039, 1.3+0.039)= (1.26, 1.34).