Question
In: Statistics and Probability
The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly...
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.
Solutions
Expert Solution
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)
orchestra answered 3 years agoRelated Solutions
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