In: Statistics and Probability
The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.40. Construct a 95% two-sided confidence interval for σ. Assume population is approximately normally distributed.
Round your answers to 4 decimal places.
Solution :
Given that,
s = 0.40
s2 = 0.6325
n = 51
Degrees of freedom = df = n - 1 = 51 - 1 = 50
At 95% confidence level the 2 value is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
1 - / 2 = 1 - 0.025 = 0.975
2L = 2/2,df = 71.420
2R = 21 - /2,df = 32.357
The 95% confidence interval for is,
(n - 1)s2 / 2/2 < < (n - 1)s2 / 21 - /2
(50)(0.6325) / 71.420 < < (52)(0.6325) / 32.357
0.6654 < < 0.9886
(0.6654 , 0.9886)