Question 5.20: Refer to Example 5.18. Assume that on the basis of a very la......
Refer to Example 5.18. Assume that on the basis of a very large number of previous measurements of other beams, the population of shear strengths is known to be approx-imately normal, with standard deviation 𝜎 = 180.0 kN. Find a 99% confidence interval for the mean shear strength.
Step-by-Step
We compute \overline{X }= 668.27. We do not need to compute s, because we know the population standard deviation 𝜎. Since we want a 99% confidence interval, 𝛼 ∕ 2 = 0.005. Because we know 𝜎, we use z_{\alpha ∕ 2} = z_{.005}, rather than a Student’s t value, to compute the confidence interval. From the z table, we obtain z_{.005} = 2.58. The confidence interval is 668.27 ± (2.58)(180.0) ∕ \sqrt{15}, or (548.36, 788.18).
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