Question 5.6: Based on the microdrill lifetime data presented in Example 5...

The confidence interval has the form \bar{X}\pm z_{\alpha / 2}S / \sqrt{n}. We will solve for z_{\alpha / 2}, then consult the z table to determine the value of α . Now \bar{X}=12.68, s = 6.83, and n = 50. The upper confidence limit of 14.27 therefore satisfies the equation  14.27 = 12.68 + z_{\alpha / 2}(6.83 / \sqrt{50}). It follows that z_{\alpha / 2}=1.646. From the z table, we determine that  α/2, the area to the right of 1.646, is approximately 0.05. The level is 100(1 – α) %, or 90 %.