- The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37. Construct a 95% two-sided confidence interval for the standard deviation

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Step 11.Given:n=51s=0.37The degrees of freedom is obtained as below:df=n-1=51-1=50From the Chi Square table, the left side critical value for chi square with 50 degrees of freedom is χ20.052,50=71.4202.From the Chi Square table, the right side critical value for chi square with 50 degrees of freedom isχ21-0.052,50=32.3574.Step 2The 95% two-sided confidence interval for the standard deviation is obtained as below:n-1s2χ2α2<σ<n-1s2χ21-α250×0.37271.4202<σ<50×0.37232.35740.3096<σ<0.4599Thus, the 95% two-sided confidence interval for the standard deviation is (0.3096, 0.4599).   ...