Question

The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.36. Construct a 95% two-sided confidence interval for σ. Assume population is approximately normally distributed. Round your answers to 4 decimal places.

Answer 1

Answer: $0.3012$

Step-by-step explanation:

The confidence interval for population standard deviation is given by :-

$s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, n-1}}}$

Given : Significance level : $\alpha: 1-0.95=0.05$

Sample size : n= 51

Sample standard deviation : s=0.36

Then by using the chi-square distribution table, we have

$\chi^2_{1-\alpha/2, n-1}}=\chi^2_{0.975, 50}=32.36$

$\chi^2_{\alpha/2, n-1}}=\chi^2_{0.025, 50}=71.42$

Confidence interval for population standard deviation will be :-

$(0.36)\sqrt{\dfrac{50}{32.36}}$