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 approximately normal, with standard deviation σ = 180.0 kN. Find a 99% confidence interval for the mean shear strength.
We compute \bar{X}=668.27 . We do not need to computes, 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_{.oo5} = 2.58. The confidence interval is 668.27 ± (2.58)(180.0)/ \sqrt{15}, or (548.36, 788.18).
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