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 = 0.46. Construct a 95% two-sided confidence interval for σ. Assume population is approximately normally distributed.

Answer 1

Answer: $0.3849$

Step-by-step explanation:

Given : sample size : n= 51

sample standard deviation : s= 0.46

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

Using chi-square distribution, the critical values will be :

$\chi^2_{\alpha/2, n-1}=\chi_{0.025,\ 50}=71.4202$

$\chi^2_{1-\alpha/2, n-1}=\chi_{0.975,\ 50}=32.3574$

Confidence interval for population standard deviation ($\sigma$) :

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

Substitute all the values , we get

$\sqrt{\dfrac{(0.46)^2(50)}{71.4202}}$

Hence, the 95% two-sided confidence interval for σ : $0.3849$